I'm thinking of cutting ties with a girl that's madly in love with me even though I think I might feel something for her
Why do you need to cut things off with her even if you think you're interested with her?
It's just not going to happen.
Even thought it can be hurtful, it is better to be honest with somebody when you don't think a relationship is going to work out. They will appreciate not wasting their time with you.
She will be pissed I annoyed her, even if I slightly like her.
At first, yes, she will be mad, but I feel like that will be better than having an unstable relationship in the long run. I do hope you tell her calmly and not make her uncomfortable in the process.