Don't care , don't mind ,doesn't matter , nevermind

"Don't care" means you don't care about what happens. It views at all.won't change your 

"Don't mind" means you are allowing it to happen.

"It doesn't matter" means you don't think it can help you, or won't affect the outcome.

"Nevermind" means forget about the fact I ever said anything.

I don't care.
As this indicates complete detachment and disinterest, it is the most emotionally-charged of the four. You can do what you like, I don't care, it is nothing to me.

I don't mind.
This is a gentle statement indicating general assent and support.

It doesn't matter.
This is often rather like I don't mind. Alternatively, it is very like never mind.

Never mind.
This carries a strong sense of forgiveness or reassurance. It's OK, I know you have done something silly, but we can make the world OK, between us.