Wunder von Skagerrak would be a war-winner
I am by no means an expert, and please do tell me if I make huge errors in the battle itself or while wondering about what it could cause. I am myself making a timeline with PoD at German heroic victory at Skagerrak.
I agree to what others have stated in this thread: There is no way that Grand Fleet could've been destroyed in the battle. However, it could've been beaten really badly if luck was on German side. This is kinda unlikely scenario, but more unlikely scenarios have happened in real life.
Let's first assume that German zeppelins managed to scout the area and spot British ships. OTL a storm prevented this. All submarines used in preparations of Jutland are contacted in time, I think there was 10 of them. Now submarines are giving chase to British main fleet.
Battlecruiser action goes pretty much like Germans intended; British seeing the German battleships too late and taking heavy losses. Remaining British ships turn towards main British fleet and start escaping. Because of zeppelins and U-boats, Germans now have accurate information on main British force.
Germans do not engage in prolonged fleet action but turn after firing a few times at the British who barely had time to go into battle formation. This time British do give chase to Germans, because the battle hadn't yet caused heavy damage on main fleets and there was more sunlight hours left.
When giving chase, British destroyers and cruisers move faster and slower battleships are at the rear of British formation, largely unprotected. German U-boat crews can't believe their luck and sink many of the battleships by surprise attacks.
There is a chaos in British formation, and when the main fleet of Germans notices this, they turn around again and engage the British cruisers and destroyers. British decide to live to fight another day and try to make a run for it, but they now have to pass the submarines, which again cause heavy damage on British fleet.
This would be a great victory for the Germans and a black day for Royal Navy. I'd imagine about 4:1 ratio in British losses versus German losses. The battle would be known as Wunder von Skagerrak and used heavily in propaganda to raise German morale through the roof. British would probably try to hide their defeat from the public.
Now, lets try to guess what this would cause in the long run. German High Command would think this means there is hope fighting against Britain on the sea openly, and not resort to unlimited submarine warfare. This in turn would cause USA not to join the war (I can't imagine a Zimmermann telegram when USA has good relations with Central Powers). This alone could be a war-winner.
Germans would focus in sea battles where submarines are used against enemy main fleets instead of blowing up merchant ships. These attacks would be almost always supported by smaller German fleets and/or Zeppelins.
Also, fighting against the British openly would cause panic in British homefront. British blockade could be broken in 1917 and Britain would concentrate on keeping its own coast safe. I do not think Germans would try to invade Britain, but British public does not know it. However, Germans can't hope for more than breaking the blockade. Channel is too heavily guarded and British harbours would be full of British ships.
Breaking the blockade and humiliating the Royal Navy could have even larger butterfly effects than USA keeping out of the war. German homefront would be pretty much safe now. Britain would panic and maybe draw some troops back home from France. This would strain the relations of Entente. However, I do not think that there would be immediate effects. Somme and Verdun would still go as in OTL.
With no USA in war, after Brest-Litovsk there would be total panic and fear of losing the war in France and Britain. Germany could plan Kaiserschlacht better and before massing troops in Western Front could knock out Greece and help Austria-Hungary to hold against Italy. Germans would wait until a panicked Entente offensive, and only after that launch what we knew as Spring Offensive.
Entente Spring Offensive would happen, as a last ditch effort to knock Germany out before superior German force would be moved completely on Western Front, and it would use early Blitzkrieg tactics and combined arms to cause some initial successes. However, it would probably be less successful than Spring Offensive OTL. A few points of Hindenburg Line would break agains fast and intense bombardment followed by hundreds of tanks and infantry advancing behind tanks.
However, tanks were unreliable and Germans already knew how to take them out. The losses in Spring Offensive would be bit heavier on Germans than Entente, but Entente would lose most of its tanks which couldn't be replaced in time and many of them fell in German hands. In the end Germans would retake Hindenburg Line, though at heavy cost, and capture many Entente tanks and artillery.
Very soon after than, Kaiserschlacht would be launched, and it would work. Entente defense would be weaker with no America, part of British army staying in Britain, and hundreds of thousand losses in previous offense. Kaiserschlacht would use Stosstruppen as in OTL, who were kept safe from front lines during Entente offensive.
Amiens and Hazebrouck would fall in Michael and Georgette respectively, and British force would have to try to hold Channel ports and retake these cities, but Germans would reinforce the positions heavily. Blüher-Yorck and Gneisenau would go pretty much as in OTL, with French forces throwing everything and the kitchen sink to halt the advance towards Paris, and mostly succeed. Germans capture only marginally more territory than in OTL.
Champange-Marne would be a huge success for Germany, with outnumbered French forces thinking all is lost and refusing to counter-attack. Large mutinies and lack of counter-attacks enable Germans to create a large salient, almost streching to Verdun. Only things stopping Germans from rolling to France now were logistics slowing the German advance and France drawing most of East army there. Peace talks between Central Powers and France and Belgium were opened in secret.
With Hazebrouck and Amiens taken, BEF logistics are almost broken. Final German push towards Paris seems like a certain thing, and everything that can be moved, is moved from reserves to form a strong line streching from Amiens to Compiegne to Verdun. However, final push towards Paris never happens, with peace talks already happening. Entente tries to break the the German salient desperately, but before British forces can be moved for the offensive, the last German push which had to be called off OTL happens; the Hagen Offensive, taking Dunkirk and pushing the British to Calais. Belgium capitulates 17th of November 1918.
While the offensives never reached Paris, France surrendered nevertheless, in 21th of November 1918. The back of her army was broken, Russia was out of the war, British forces were limited to north of France, mutinies and revolts were happening everywhere, money had ran out, and German shells were already hitting Paris. As soon as France capitulates, German troops are given permission to move over French territory.
With everything collapsing around them, BEF evacuates to Britain. Some shots are exchanged over the Channel, but everyone knows war is over. However, Britain is pretty much safe, and agrees to white peace with Germany in 1st of December 1918, and returning most of her colonies in Africa, with no other reparations required.
Last Entente powers in Europe, Portugal and Italy, capitulate in 12th of December 1918, when German troops threaten Italy from France. China, Japan and Brazil and other Entente powers across the globe surrender in 22th of December 1918, in so called "Christmas Peace". Peace treaties against France and Italy were Versailles-level rough, but everyone else survived with very minor reparations, because at this point no one wanted war anymore and Germany really didn't have the ability to project power across the world.
After that there are way too many butterflies in the air, but you can try to read any of the many Central Victory 1918 timelines.