Evict vs “Good Cause to terminate the lease"

[Stephen Homes]

I have a section 8 tenant in New Jearsey. To name a few she damaged her unit and the unit under her and not willing to pay for the damages that she caused (I had both places fixed). Changed the lock without my knowledge and will not give the key to it. Open my mail. Not let contractors and handyman do work make the inside of her unit and outside very dirty and so on. 

To minimize my loss, I want to make sure that section 8 continues to pay me while she is in the unit till I get her out. 

Is it better to evict her or send “Good Cause to terminate the lease" to the tenant (and a copy to section 8) and have section 8 transfer her to another rental? Thank you