Which task involves sealing off an enemy to deny them external support?

The task that specifically involves sealing off an enemy to deny them external support is isolation. This strategy aims to cut the enemy off from reinforcements, supplies, and other forms of support that could empower them in battle. Isolation is crucial in military operations as it seeks to weaken the enemy's position and capabilities by restricting their access to resources and allies.

In contrast, occupying typically refers to taking control of a specific area, securing focuses on protecting or defending an asset or space, and following and supporting involves maintaining a presence to assist or bolster operations rather than cutting off enemy assistance. Hence, isolation stands out as the most accurate choice for the described task.