Would throwing a heavy object in space work as a form of propulsion?

Yes. For two reasons.

When you throw something, there is a force exerted on you just like you exert a force on the object you throw. Momentum is conserved, so whatever momentum you give to the object you throw in one direction, you gain from the object in the opposite direction.

The first reason you want to throw something heavier is that when you apply a force on a heavier object, it won't have as much of an acceleration as a lighter object. Thus, you can push with the same force that you'd push a lighter object with, but for longer, since the object won't fly away immediately. And since you applied the same force but for a longer period of time, you'll have delivered more momentum to object you pushed, and will have gained more momentum in the opposite direction.

(When in trouble, think of the extremes - a person throwing their watch versus pushing off a massive wall)

The second reason you want to throw something heavier is that the lighter you are, the faster your velocity will be with the momentum gained opposite to the direction you threw the object. By getting rid of heavier things you're carrying, it'll be easier to accelerate with any amount of force applied - you'll have a higher velocity with any momentum you gain.

The force on the, let's say a watch, would be equal to the force acted upon the person due to there always being an opposite and equal force. Given two objects expelled from a person at the same velocity, the one with bigger mass would result in the person having higher velocity.