脱(tuō) - to take off, to shed, to come away in Mandarin

脱 (tuō) is the verb for removing something that was on you: 脱鞋 take your shoes off, 脱衣服 undress, 脱帽 take your hat off. It is the exact opposite of 穿 and 戴, and Mandarin keeps that pairing tight, so if you put it on with 穿 you take it off with 脱.

The second sense is coming away or falling off by itself, without anyone doing the removing. Hair, paint, skin and book covers all 脱. That is where 脱皮, 脱色 and 脱发 come from, and it is why the word also sits inside 脱离 and 逃脱, where the thing escaping is coming away from what held it.

The trap is the English phrasal verb. Take off in the aeroplane sense is 起飞, never 脱, and take off as in leaving quickly is 走 or 跑. 脱 only ever means something separating from a surface, and in the clothing sense it needs the garment named, so 我脱了 alone reads as undressing rather than departing.