What is the type of offensive operation designed to catch or cut off a hostile force attempting to escape, with the aim of destroying it?

The type of offensive operation designed specifically to catch or cut off a hostile force attempting to escape, with the goal of destroying it, is known as a pursuit. In a pursuit operation, the attacking force maintains pressure on the withdrawing enemy to prevent them from regrouping or escaping, ultimately aiming to eliminate them or force them into a position where they can no longer effectively resist. This tactic is characterized by the rapid movement and aggressive engagement of the enemy, leveraging momentum to exploit any weaknesses in their defensive posture.

Pursuit operations are essential in maintaining the initiative during combat and can lead to significant operational successes, particularly when an enemy force is in a state of disarray or retreat. By executing a pursuit, a force can take advantage of the enemy's vulnerability, aiming for complete destruction or capture of the forces attempting to escape.