I have a '90 Corvette. I know it's not a third gen but I think that this is the best place to look for the anwser.

Why does my car want to stall when there is no VSS signal?

It idles normally but when I drive and want to stop, the engine almost stalls.
I have a bad VSS so it takes some warming up for it to start to work.
But as soon as I see mph readings, everything comes back to normal and
there is no stalling.

 

the VSS input is used for the dash pot effect.
meaning that as you come to a stop the ECM opens the IAC a little to help prevent stalling.
i forget at what speed it opens the IAC, it seems like its around 15 MPH, or around 20 KPH for you.
also, the ECM uses the signal for fuel control. without a speed input the ECM stays in cell 4.
there are a few other things the ECM uses the VSS for, EGR and canister purge and it seems like a couple or other things i don't remember right now.

 

Thank you!