So a second chainsaw in the opposite direction?

If the chainsaw generates so much inertial that it challenges your trajectory, you're doing something right.

an equal and opposite angular momentum

Idea: contra rotating chainsaws.

You can balance it adjusting the rocket nozzle

just enough rotational velocity to counter gravity trying to pull the nose of the missile down though. and also the centripetal momentum of the chain would act like a gyro stabilizer insuring that it remains nominally upright.

The real one deploys blades that cause the missile to spin at very high speeds before it slices through its targets like butter without an explosion

nuh uh, make it laser guided