If both sides wanted a break (i.e. Kostitsyn wants to go to Russia and Nashville doesn't want him anymore), they absolutely can mutually terminate his contract. I'm not sure if you have to first assign him somewhere and have him report or not, but if both parties agree the player can go on termination waivers and, provided he clears, the contract is gone. Nashville would have no cap hit but Kostitsyn wouldn't get any money. Montreal just did this at season's end with Alexander Avtsin. Avtsin wanted to back to Russia, so Montreal put him on termination waivers and terminated his contract the next day.
Five players were placed on termination waivers this year: Avtsin, Alain Berger (also by Montreal), Nick Petersen (by Pittsburgh), Corey Elkins (by Anaheim) and Niko Hovinen (by Philadelphia), all but Hovinen had their deals terminated (Hovinen was claimed by Edmonton and assigned to their AHL team, where he is still dressing as their back-up). Avtsin, Berger and Elkins all left their NHL teams for teams in Europe, while Petersen signed an AHL deal with Houston (It's been speculated that his termination had to do with his wife's health problems).
So, yes, it is possible to have a contract mutually terminated. It very rarely happens to well-known players, though, because no player wants to walk away from that much money. I believe John LeClair was the most well-known player to go through this process back in 2006, his last year in the NHL. LeClair was unhappy, Pittsburgh was unhappy, he didn't want to go to the AHL, so the two sides agreed to terminate his deal and he became an UFA.
