Resident allowed water & electric to lapse. Allowing dog to poop on floor. Resident 39 days late on rent. Can I legally get some sort of fast eviction due to breech of lease?

What state are you in?
You most likely have to give them a written eviction notice according to how many days your state requires. Then if they do not move take them to court.
Some states have as little as 3 day evictions.
If you have to take it to court specify that it is not only because of the rent because many states if they pay up they stay.

Indiana

Indiana Evictions (http://www.rentlaw.com/eviction/indeviction.htm)

I will get back with the time frame and what you have to include in a notice if somebody else doesn't before I get back on here.