RealGM

If a player signed to a multiyr contract is waived by a team, how many years does the team have to play him?

for example, if Miami waived Mark Blount, how long would they have to pay him?

Unless they negotiate a settlement of the contract (a "buyout") for less, they have to pay him every cent of guaranteed money in the contract, including option years the player held. They don't have to pay him any non-guaranteed years or team option years.

Most NBA contracts are fully guaranteed, so lacking any options, if a player is waived now with a contract for this season plus two more, it's most likely going to be the rest of this season, plus the next two, that he gets paid.

As I understand it, they don't have to pay it up front when they waive him - they pay him as if he was never waived, unless there is some provision in the contract or buyout that says otherwise in the event of waiver.

The only thing to add to FGump's explanation is that if the player has a Player Option, then the contract contains a paragraph dictating whether he gets paid for the option season if he is waived before the option is invoked.