Can I evict tenant for dog on property?

[Saad Handoo]

I had a tenant violate the terms of my lease by keeping a pet on the premise. The pet happened to be a pitbull who jumped my fence and injured the neighbors dog. I live in another state from my rental property and received a letter from the neighbor essentially putting me "on notice" so that they have a paper trail in place if the issue arose again and they needed to take legal action. They claim the tenants to be hostile people and that the dog has attacked other dogs and upset the whole neighborhood. 

I've confirmed through an inspection that the dog is no longer on premise and has been removed. Should I go a step further and tell the tenant they have 30 days to vacate my property otherwise they will face an eviction?

Would love everyone's thoughts. My inclination is to remove the tenant but who is to say the next one won't have some problems associated with them as well.