Should I break up boyfriend for hitting me?

My boyfriend punched me in the face yesterday when we got into an argument, and now I have a black eye. This morning he told me how sorry he felt and asked me to forgive him. However I'm thinking of breaking up with him, for my own safety, but he has mental health problems, and I feel guilty for leaving him. What should I do? Should I forgive him?
Updates:
1 mo
I broke up with him, thank you for the support/advice
Should I break up boyfriend for hitting me?
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