Hey there, 할 수 없지, 뭐 is just a way of saying 'Okay, then', 'It can't be helped', 'Suit yourself'... etc. It is a correct phrase. Hope this helps! :)

thank you...

"(그것은) 할 수 없지, 뭐!", Here, the word '뭐' is an interjection. It is just used to show that the speaker accepts that situation even though he/she feels disappointed, like "well" in English. Other examples : "뭐, 어쩔(or 어찌할) 수 없지", "뭐, 별수 없구나"