Infested compost

I have a plant about 3.5' basically a complete gonner. Infested with spider mites all the way up to the top leaves. all treatments only slowed the mites down. Now my plan is to carefully chop it into bits and mash it into my compost. NOW is this not a good idea? Will they continue to live eating organic mater in the compost or will the heat and bacteria just kill them?

I'd neem the living shit out of them. The worst that could happen is your plant could die, but you plan on killing it anyhow, so there is no loss. Yes, when your pile heats it will kill the mites.