The process by which the ocean floor sinks into the mantle is called

Subduction

Explanation:

Subduction is the movement of the tectonic plates such that the downward and sideways movement of the plate's edge results in the in the sinking of the plate that is pressed below by other plate into the mantle.

This sinking occurs as a result of the huge amount of gravitational potential energy.

This process occurs in deep ocean trenches and takes place at the plate's convergent boundaries.

The zone where the process of subduction takes place is referred to as subduction zones.