I have urges to cut all the time and it is not because I am suicidal it is just away to feel. But I would at least talk to someone about the thoughts that you are having. I would worry that the thoughts would become to strong to ignore. You are strong to over come this. ((Hugs))

I think only if you are going to act on urges to kill yourself that you are suicidal. Like, you can have thoughts about suicide or dying without being suicidal. If you know what I mean.

The urge to cut is not the same as being suicidal otherwise I know a lot of people in my community with otherwise healthy lives that are suicidal.

Cutting is a coping skill (albeit a crappy one) for dealing with pain, stress, sadness, depression or other strong emotions that are too much for our psyche to handle. Cutting, unless aiming for major arteries like jugular, ventricle.or any other major artery, is not generally a suicide attempt and most medical professionals know that.

No it doesn't mean you're exactly suicidal, but if the thoughts become persistent and don't go away talk to your doctor about them. The moment you get the urge to actually act on it go to the hospital. But only if you get the urge.
For me, I went to the hospital when I literally formed a plan and tried acting on it. So, be concerned if you actually form a plan.