As other members have pointed out, phrasal verbs can have quite different meanings, depending on the context. I guess you're asking about stopping an unhealthy habit. You would say "give up smoking" but not "cut out smoking". The "cut out" in this context means "remove (from something)". You can give up chocolate, but as for cutting things out, I'd sooner say "cut out fatty foods from your diet". It seems a little more natural to use "cut out" in a general sense here. That's just my impression.

Hi! Phrasal verbs are difficult! 'Give up' means to stop doing something usually without finishing it. For example, 'She didn't want to give up running but her knees really hurt.' http://www.merriam-webster.com/dictionary/give%20up 'Cut out' can mean two things- 1: stop doing something, usually referring to something annoying. For example,the mom said to her two children who were fighting: 'Cut it out!' 2: 'Cut out' can also mean to remove something. For example, 'I cut out sugar from my diet'. I hope this helps! I'm happy to help you with any further questions. Amy http://www.italki.com/teacher/1788721

Hi, Antonio, They aren't quite the same. To give up means that you're quitting the situation--like, "I just can't figure out how to do this, so I'm going to give up." (Also, in English you give up on something or someone-- "She wasn't reliable, so I gave up on her.") "Cut out" can mean different things. Very colloquially, it can mean to leave quickly--"The party was a drag, so I cut out early." There's another phrase, "cut it out," which means "stop it!" That's probably the one you mean: "He was annoying me, so I told him to cut it out!" It always functions as a unit, though--you wouldn't say "I cut out doing that." I hope this makes sense!

"Give up" means that you are done trying. Example: "I give up on trying to put together this puzzle." On the other hand, "cut out" means something different. To cut something out of your life means that you no longer want it and you are getting rid of it. Example: "I'm cutting caffeine out of my life." I'm no longer going to drink drinks with caffeine in them. I'm cutting it out. Also, there's an idiom for it as well. If you tell someone to "cut it out", you are telling them to stop what they are doing. Example: "My brother was bothering me, so I don't him to cut it out!" Hope this helped! -Kyle