「いっぺん」 = 「[一回]{いっかい}」 = 「[一度]{いちど}」 = "(for) once"
Now, onto 「シメる」. When you see a verb that sounds familiar but its stem part is written out in katakana, the chances are that you are seeing an informal or slangy verb. 「シメる」 is no exception. It comes from 「締める」= "to tighten", "to be strict",etc., but not 「閉める」= "to close".
*Note that this occurs only with the Yamato verbs, not with Sino-loan-verbs that end in 「する」.
(Verbs such as 「アピる」= "to apeal", 「ディスる」= "to disrespect", etc. technically belong in a different category of verbs, obviously, so I am not including them with my statement above regarding Yamato verbs even though they are also written out in the 'katakana + る' format.)
「シメる」, IMHO, has a perfect English counterpart for both meaning and nuance (and even slanginess) -- "to put the screws on (someone)". You do not have to be a gangster to use 「シメる」; We use it jokingly quite often.
「シメんぞ」 is just the Kanto colloquial form of 「シメるぞ」
いっぺんシメんぞ、おまえら。
therefore, means:
"I'll hafta put the screws on you guys for once!"