The problem with the mercenaries winning the Mercenary War is that Rome had a vested interest in keeping Carthage alive, because of the indemnity Rome forced upon it in the treaty after the First Punic War. While, yes, Rome did take advantage of Carthage's weakness to annex Sardinia during the war, it also rejected an opportunity to annex Utica, and nominally helped Carthage by returning nearly 3000 prisoners to it during some of the darker days of the war. So if the mercenaries become successful enough to besiege Carthage itself, you might see Rome intervening on Carthage's behalf, just so that they can ensure they're going to get their money. Rome being responsible for Carthage's salvation could have all sorts of implications....
However, assuming Rome stays completely out of it...
I think a good POD for Carthage losing the Mercenary War might be the Battle of the Bagradas River - there, Hamilcar Barca pulled a risky maneuver where he feigned retreat, urging the much larger rebel army to give an undisciplined chase, before turning his forces around and slaughtering them. Here we'll say the maneuver fails and Hamilcar's army is crushed, and just to add the cherry on top Hamilcar dies as well, thus depriving Carthage of its best general.
I think you do need to have Carthage sacked for the mercenaries to win the war, and I think you can define a mercenary victory as the establishment of a mercenary state in Africa. Its captains had went past the point of no return; the mercenaries were minting their own coins, and a huge part of its strength was built on the Libyan peasantry trying to gain some power. A victory like the one I described might bring more of Carthage's allies to the mercenaries' side. Maybe they could get a slave rebellion going to? (Miles mentions that it was "striking" that the mercenaries never tried to incite a slave rebellion) Sacking Carthage would be very difficult for the mercenaries to accomplish, but I think it can be done, provided the rebels are willing to wait out the year or two it would take to see the siege through, and that Rome doesn't bail Carthage out.
Some kind of arrangement would need to come between the mercenaries and Rome. I doubt that the rebels would take on Carthage's debt. Maybe Rome is allowed free reign over Spain as compensation? I could see the Punic cities in Spain asking for Roman protection without Carthage anyways. That in turn probably leads to Rome trying to conquer all of Spain during the period of OTL's Second Punic War. Sans Carthage, we might not see a Roman conquest of Africa for a long time... maybe an earlier conquest of Gaul instead? As for the mercenaries, I have no idea what such a state would look like. Matho declaring himself king? Some kind of republic? Either seems possible. Regardless of its government, I think it would be confined to just Tunisia though. I don't see Carthage going on as an independent state if the mercenaries have their own state.