Sometimes, life is hard

[TranquillityBase]

You can’t expect me to spend that 
            on a cat, teeth rotting.
She isn’t eating, can’t you fix her?
 
He bit a child, this happy go lucky
            two-year-old pitty.
Ten-day quarantine or decapitation,
            that’s state law.
The trick is to find the angles between
            the vertebrae
to sever the ligaments.
 
A piece of me goes to the lab
            for testing;

a fabric worn bare,
about to tear beyond stitching.

Is " pitty" a typo, or a bit of slang I just don't know?

Don't quite get connection between last line and the poem.

Third stanza is my favorite.  It could stand alone.

Yeah, this one is sparse.  I was afraid the last lines would be confusing.  'Pitty' is slang of sorts for Pitbull.  Before I try to edit too much, I am wondering what you think the poem is trying to convey.  Thanks for reading, TqB.
bryn

Ooops, I meant second stanza is my fave and could stand alone.

I'm not too good at explication, but I'll give it a shot: people and the issues they face in their relationships to their pets; pets have a hard life, dependent as they are on the goodwill of humans; the fabric worn bare would be a pet who has done something, like the pit, or simply gotten old and expensive to keep alive, in the first stanza.  That's what I'm thinking it's about.  Obviously, the examples portray our humanity at its possible best (or worst).  But central characters are the pets themselves, so it elicits sympathy for them in me.

Hope that is some help.