I can't claim to understand why someone would want to cut themselves in such a way. I can say I do know how it feels to want to die from things affecting me. But, firstly you say you think he likes a woman, but you don't know. Sure some can say feelings are based in fact, but when you're dealing with distress, like you seem to be, feelings can be a bit tweaked.
Have you ever sought help for the self harm? If not, I would suggest it. I came close to ending it more than once, each time something silly or stupid saved me. I thought I'd be weak if I asked for help, found out I was weaker not asking. I still battle it, almost every day. But with help, therapy and tools I never knew about, I've kept the fight going and found there are things out there that are worth hanging around for.
You say you'll die alone, but I promise you, that's a feeling a lot of people have. I had it in the past and though they are gone, I'm still here. Alone isn't terrible, being with someone that doesn't appreciate you, that doesn't care, that doesn't understand you is worse.
I can't say this is the situation you're in because all I have to go on is that you "think" he likes someone. Self doubt can lead to assumptions that can tear you apart.
If you can, please either talk to him or seek help from someone that has the tools to guide you. You are worth so much more than you might think or feel. 🤗