You'd better not tease her. She just downed three beers.

Literal

Her tease not [better-方がいいよ]. Three beers [object-を] drank-up [just-ところだから].

からかわない方がいいよ advises against teasing. 3本ビールを飲み干した means 'drained three beers.' ところだから means 'because she just did.' A humorous warning.