It is possible that a blood clot in your leg explode, causing your leg to be amputated?

Actually....yes: A very rare complication of extensive DVT is a condition called phlegmasia cerulea dolens, where the clot effectively cuts off the arterial supply to the leg, and this can result in amputation. This is very rare.

Yes, possible.: Any vascular compromise can result in the need for an amputation.

Would not explode: But if in the artery could cause vascular compromise leading to amputation.