JasonAC556 at the PerfectUnion BBS provided the following instructions for removing the old rear sight, which worked:
1. Take a small punch and remove the pin that holds the windage screw captive. You will see it on the right side of the sight assembly as you shoulder the rifle.
2. Depress the windage adjustment pin on the left side of the assembly and unscrew the windage adjustment knob until it slides free of the assembly. Be careful to keep the adjustment pin captive so it doesn't fly across the room.
3. Carefully lift up on the back of the sight assembly. The elevation adjustment pin spring and pin will drop free from the bottom of the sight assembly, so be careful not to lose these.
4. You're done!!
I wanted to reproduce the instructions here so that it'll be easier to find by others.
I'm looking forward to getting the Mini-14 out and zeroed.