To Escape
To Flee
する verb
You escape and run the hell out of there. Basically, you're trying to escape or to flee. Pretty simple.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. The だつ changes to だっ, though, so be careful of that.
どうやって脱走に成功したの？
How did you manage to break out?
犬が脱走しないように、フェンスを作りました。
We built a fence to prevent the dog from escaping.
重い刑罰を言い渡された犯罪者が、刑務所から脱走した。
The criminal, who had received a heavy sentence, broke out of prison.