I know I've played the game enough I should know this. If my player cleared waivers before the trade deadline, am I still responsible for his salary if I cut him? I'm sure I am, I guess this is wishful thinking

Yes, you are.

You are responsible for the player's salary for the remainder of the contract unless someone else picks him up. If claimed off waivers, the new team is responsible for the rest of the contract. If signed after clearing waivers, the new team will only pay the prorated of the league minimum salary for the remainder of the season and the league minimum for ensuing seasons on the contract.