I like your approach but first I would get counseling and talk through the best way for you to resolve your relationship with your mother...you may end up writing a letter or doing something quite different...give it some thought with a professional.
I also wanted to add that I have cut my arm (not suicide, but self mutilation) twice because of some hard times in my life. No scars, but a relative of mine said it was odd behavior.
I had someone very close to me that used to "cut" themselves on a regular basis when they didn't want to deal with emotional pain they were going through. I didn't understand this at the time, but learned through watching her go through treatment that this is a disorder that needs to be dealt with promptly. The idea was that someone cuts themselves physically to experience physical pain vs. emotional pain. It's very sad that you have had such a rough relationship with your mother. But no one is worth letting yourself feel this way and getting to the point that you are doing yourself harm. Your mother isn't the one that is getting hurt over your lack of a relationship, you are, and you need to release yourself from that need, because most likely you will never have the type of relationship with her that you want. Giving birth doesn't make someone a "mother" but years of caring and giving do and you can't make the past be different and doubtful that any future relationship won't be either.
Hang in there and take care of "yourself"
Thanks to both of you. That was great advice.
I too have a friend who cuts herself and says to me all the time "I cut myself to bleed out of this body that I hate." At the time I was in a odd state of comfort, but then as I thought about it her approach made sense, but wasn't healthy nor right. I'm always trying to help her out, but sometimes it's hard because they're so driven to their problem that they believe there's no comfort in trying to change your habits and ways, but in the long run there is.
Anyone that has someone who cuts themselves you must act quickly on getting them help otherwise it maybe too late and they may do suicide.
I would definitely seek counseling. I, at one time, was climbing the walls with anxiety and sought counseling and it helped me immensely, along with medication from a psychiatrist.
They will give you coping information. Good luck!