How do you remove the rotor form a 1989 323 Mazda?

I assume you mean the rotor for the distributor. It is held in place with a small Phillips head screw. Take of the distributor cap (held in place with two Phillips head screws). Turn the engine over until the contact portion of the rotor is pointing down. Unscrew the machine screw from the rotor arem and pull the rotor off the distributor shaft.

If you are refering to the brake rotor, you will need to jack the car up and support it on jack stands. Remove the road wheel & tire. Have someone step on the brake pedal, and undo the nut holding the half-shaft to the hub assembly. Remove the two bolts holding the brake caliper to the strut. Remove the cotter pin and undo the nut of the tie rod from the hub assembly; uncouple the tie rod end from the steering arm of the hub assembly. Undo the bottom pinch bolt (holds the axle carrier to the lower ball joint). Remove the top two bolts of the axle carrier/brake rotor assembly. You can now take the axle carrier/brake rotor assenbly off the car.

Working on the bench, bend back the loaking tabs for the rotor retaining bolts, then remove the retaining bolts. You should now be able to remove the brake rotor from the hub. Note if you have committed to replacing your brake rotors, you will probably want to repalce you hub bearinsg and seals while you have these assemblies off the car.

Also be sure to inspect your lower ball joints and brake pads and replace if worn.

CheersMalcolm