Should I cut her out of my life?

Ankind
For quite a number of years I have been friends with this girl. She's really nice and very good looking and we get along well. Over the past 6 months I've become increasingly attracted to her, so much so I cannot stop thinking about her. A few days ago I summoned up the courage and asked her to be my boyfriend, she rejected me and gave me the whole "You're such a nice, guy; I'm hoping we can be just friends" treatment.

I am heartbroken, soul crushed and very angry.

She says she still wants to be friends with me and said she never meant to hurt me but I don't know if I could handle being around her anymore. This may sound rather cruel but I'm thinking that if she does not want to be with me, I don't want to be her friend.

By cutting her out of my life I mean completely: don't talk to her, avoid her in social situations, block her number and Facebook and forget about her. Treat her like she doesn't exist.

Close friends say that me cutting her out would really upset her but her rejecting me has hurt me. I don't know what to do.

What should I do? Should I still be friends with her? Or should I cut her out of my life completely?
Should I cut her out of my life?
5 Opinion