What happens to an object that is moving in a circle if the centripetal force is removed?

The centripetal force is what draws the object towards the centre.

The centrifugal force is what draws the object away from the centre.

Generally when one speaks of centrifugal force, one means only that it takes the centripetal force to keep moving the object out of its straight direction of travel.

If you remove the centripetal force in such an example, such as when the object is in a circular orbit around another body, then the result will be that the orbiting body will continue traveling in a straight line at a tangent to the circular path it had been following.