To use something to the utmost (use it until it's worn out); also to exploit or overwork someone (colloquial).
古い傘を穴が開くまで使い倒した。
I used the old umbrella until it developed holes.
彼は新品のパソコンを仕事に使い倒している。
He puts his new computer to heavy use for work.
上司は部下を使い倒す傾向があるので、注意が必要だ。
The boss tends to overwork his subordinates, so caution is needed.