It can be purged, though unreliably, so that's an option. Nukers will probably not have too high resistance, so it'll mostly just be the flat chance to stop it. Mostly I just try to tank up as much as possible and weather the storm. Strengthen, def up, shields, revive on death etc. Bombs are supposedly the counter, but unless you have a champ that can place 1 turn bombs, chances are they won't trigger until after the enemy has already taken a turn (unless you also have a skill to reduce the bomb counter and have time to take double turns). The problematic part is not knowing whether someone will have stone skin on or not when you pick the fight.

So there are a few ways:

1) Champs like Yumeko, Warlord and Basher to lock down the enemy teams skills even through Stoneskin. Lock the enemy skills down, then take out the ones who don't have stoneskin first.

2) Double buff strip teams. So something like Arbiter into Sethallia into Serris into Magnarr. You get two 50/50 chances to strip the Stoneskin buff in this setup. Then you nuke em off the board.

3) Stoneskin or Ally Protect yourself and go secondest. Stoneskin teams love to go second and kill you for having the audacity of going fast. So you respond with champs like Seeker, Duchess, Sandlashed, Ursuga, Nekhret, Krisk.... put someone in Shield set or Bolster or both.... ignore what they are doing, let them run out their buffs, and then nuke them.

The best way is with bombs, specifically, with Gaius. He was a fusion, so I assume most people have him. Place him in the second position on your team and then even if they wipe your entire team in a single nuke, you will still win. 

I agree with the suggestions, but it ignores one thing- you need to be able to guess the team is a stoneskin team :)

If i suspect a team is a stoneskin build team (stoneskin gaius seems common) then i bring in yumeko and lock their skills out until stoneskin is worn off.

I'm just running Basher all the time now, tbh. Stoneskin teams are everywhere. 0_0

Kimi > Ramantu > Warlord > Leo 

Thank you so much everyone for the helpful tips, I'll have to try some of these out. Still very irritating dealing with Stone skin gauis in almost every arena defense but this info should help ease the stress a little bit at least.