看到stackexchange上的一个回答
beat it来自beat a retreat打退堂鼓的意思： comes from "beat a retreat", which itself comes from the use of drums to signal soldiers to leave the battle field.
所以延伸为“算了吧”，“避开它”之类的意思。
StackExchange链接:
The meaning of: "Why don't you just beat it?"
