Dealing with difficult people

One month in a new job and I am already so frustrated at a colleague that I want to break stuff! Is it really unprofessional if I tell her to shut her mouth up? This is what I think constantly when we have to talk or when I read her emails. 

She is condescending, arrogant, pushy, negative, and thinks her way is the only best way. Offer advice when, she is not asked. She thinks because she is older, she should not respect younger minds and ideas. She does not understand that if you want to play a role of a mentor for some one, you should practice active listening and you should be respected by your mentee; otherwise, it is not going to work!