tie up 有捆绑的意思，be tied up with sth 就是被某件事所占用，忙得脱不了身。

【例句】
He's tied up with his new book. He's working hard, you know. 　　
他正忙他那本新书--你要知道他现在确实很努力工作。 　

I'm tied up with work right now.I'll get back to you later. 　　
我这会脱不开身。一会儿忙完就去找你。