Is there a trick to removing the left mount? I think it's technically a transmission mount...
I got the bolt out and nut out, but it seems like it's fastened to a larger plate below it and I can't pull it out...
What am I missing?

 

If it is the transmission mount it is the 'right' mount. Left would be the engine mount. Left/Right are identified by how you sit in the car, left side is left, right side is right.

To remove the trans mount, it usually requires lowering the transmission.
I would remove the through bolt on the front and rear mounts and loosen the through bolt on the engine 'left' mount. Support the transmission with a jack and slowly lower the engine/trans enough to remove all three trans nuts after removing the through bolt.

Remove the assembly and replace the trans mount on the existing plate.
IIRC you cannot gain access to one of the nuts from the plate and have to remove the piece as an assembly and then replace the mount on the plate.
bit of the PITA, but you should be able to get away with not having to unhook any other components, just don't drop the trans as you could damage the axles, fuel lines, and exhaust.