。。
Let's have a contest. Whoever hurls the worse verbal abuse wins.
Literal
Match [obj-を] let's-do. More terrible verbal-abuse [obj-を] spat person [subject-が] win is.
しましょう is the polite volitional 'let's do.' より酷い uses より as 'more' (comparative modifier) without an explicit 'than X' — i.e. 'whichever is worse.' 暴言 ('violent words / verbal abuse') is a noun. 吐く ('to spit') collocates with words: 暴言を吐く ('to hurl verbal abuse'), 嘘を吐く ('to tell a lie'). 方 ('side, person') used with が marks the winner of a comparison. The absurd, playful premise makes this sentence engaging despite the base vocabulary.