Problem is just that. When I put the car in reverse and hit the gas pedal (softly of course), the engine/transmission makes a clunking sound in my 93 SE. It sounds like it'* coming from the driver'* side. There are no clunking noises when I hit the gas when the car is in drive.

I think it'* a transmission mount that'* broken; is there a front and rear mount on the driver'* side for the transmission? And what'* involved in changing it (if you guys think it is the problem)?

Has anyone else ever heard/seen this happen? Thanks...

Yup that'* one of your mounts. The next question is which one though right? The most common one to go is the rear Trans mount. It'* located by the firewall on the Driver'* side on the subframe crossmember.
The next one to go is the wishbone one on the passenger side, by the firewall on the other subframe crossmember.

Will it damage anything else if I don't fix it immediately?

Also, what'* involved in changing those mounts?

Mine does the same thing, haven't fixed it yet.