I know in you can not evict for nonpayment at this time in most States but if you are in a State that has a moratorium and the Tenant(s) damage the property can a landlord evict? 

Usually yes. If a tenant is damaging property, causing safety issues, drugs, etc  that violates your lease you can still file an eviction on those counts. But, you have to make your way through a bogged down court system. 

Hello there.  Will from what I was told.  My Tennant is not damaging anything but they purposely not paying any rent, u think it they are breaking out.  eg having extra ppl living there,  has a dog, taking up extra parking spaces the list goes on.  I was informed that after 6 months of non payment I can and will be taking her to small claims and yes I can evict her.  But only after 6 months of non payment and and she has a full time job.  And I have her ss number and proof of her working I can do this.  Not all lawyers know or care to keep up to date on these things.