If the money was not paid promptly, the gangsters would put a man out of business by destroying his shop.

【翻译】如果不及时支付这笔钱，歹徒就会（通过）毁他的商店，从而使他破产。

out of business：“失业；破产”，固定习语。

put sb. out of business：“使某人破产”。

by destroying his shop： “通过毁坏他的商店”，为方式状语。