If a player is released with multiple years left on contract, I understand that the team releasing the player is responsible for paying the contract for the current season of release.

How about for remaining years in the contract? That is paid by the team claiming the player, right?

Nope. When you outright release a player you retain the full value and duration of his existing contract. He still counts toward your team's salary the entire time.
Any other team who claims him off waivers gets him for the veteran minimum salary - I think, also for the duration of the existing contract.
Bottom line is that you get absolutely nothing out of an outright release unless you really, really need to clear the roster spot. And someone else gets a bargain contract on top of it.

Thanks damag. I had to offer an SP a 5 yr contract thru age 40 and his make up is only 78ish. I expect he will be useless half way thru the contract. Hopefully the ba$tard wins me a title and retires gracefully before then. Which is another question I guess. Do we know if players under contract retire sometimes?

never seen it happen when there are remaining years on a contract

With a 78 makeup if his ratings are good you'll find a spot for him. He can always mopup. Also sometimes owners will take guys like that if you throw in a prospect. There is always an option outside of outright releasing a player.