My neighbor has cat who gets loose and comes into my house all the time but Im sick of her I want her gone

This cat is from a neighbor and the neighbor lets the cat out. I'm not even sure if the cat is from my neighbor but the cat always comes to my house as if it were mine. I didn't even have a cat it just showed up one day at my door. I started to get used to the cat but I'm sick of it. It always wants to cuddle but I'm not into it. I'm into having a cat that can hunt mice but wasn't given that cat. This cat is useless it can't even hunt anything it's horrible. I'm sick of it and don't know what to do. I don't want to give it away but I'm really sick of it. I tried to kick it out but it keeps coming back. I don't know what to do anymore I'm at my wits end.