This question is posed to gauge how you handle difficult and potentially awkward situations. Make sure you understand the gravity of letting a team member go. Express how you would show empathy while still keeping to what the company needs.
Example Answer
While letting go of a team member was always a difficult decision, sometimes it was the best thing for the team, and the company. When letting go of a team member I always found time to speak with them privately. In one specific case, one of my team members had been considerably late far too often, and regularly underperformed in the workplace. Motivational discussions did little to help him improve, so the company and I made the decision to let him go. After thanking him for his work, I calmly and empathetically explained to him that he was being let go, and why. I then allowed him to finish out his posted schedule that week, before I removed him from our system.