What does "split you" mean?

Good q Ori. Suppose digesting the venom slices you in half. Or maybe explodes inside you

It means to cause mental and or emotional pain; distress.

Here's the fuller quote:

BRUTUS

All this! ay, more: fret till your proud heart break;
Go show your slaves how choleric you are,
And make your bondmen tremble. Must I budge?
Must I observe you? must I stand and crouch
Under your testy humour? By the gods
You shall digest the venom of your spleen,
Though it do split you; for, from this day forth,
I'll use you for my mirth, yea, for my laughter,
When you are waspish.

Cholericness or iracibility was thought to have to do with the spleen, hence the word "splenetic."

Thank you both.
Does "Must I budge?" refer to "Do I have to make way for you?"?

It means "to acquiesce, indulge."

And "Must I observe you" refers to "Must I pay attention to you"?

It seems to mean something more like "Do I have to see this?". "Do I really have to put up with this?"

Cool.
The nuance of "Under your testy humour" also evades from me. Does it mean "beneath your peeved influence that is so-called humor"?

Yes, a pretty good rendition.

It indicates the emotional pain or stress.

Thank you guys.
Does "By the gods" refer to "God be your witness"?

A2k'ers like Blue, Mac, and Tutor do so much better at this than I--despite my snooty BS in Journ and a lifetime writing

Keep at it fellas