How can I make a player create holes in a 3D object through tracking the navmesh agent's movement?

I'm just starting out with Unity to create a 3D game. Basically the player is an ice skater and their main goal is to create loops around enemies in order to cause them to fall through the ice. I've set up the ice rink with navmesh and use a navmesh agent to allow the player to click and glide the character.

Now my problem is how exactly can I allow the player to create holes in the ice by looping the character around the enemy?