A more appropriate and polite English expression to convey a similar forceful demand for silence without using profanity would be “Shut the hell up!” (though still somewhat vulgar).
If you want a completely non - profane and more socially acceptable way to say it, you could use “Be quiet, please!” in a more stern tone, or “Stop talking right now!” which is more direct and firm but not as offensive as the original Chinese phrase with the profane word.
The direct and vulgar translation of “他妈的给我闭嘴” is “Shut your fucking mouth!” but this is extremely rude and should only be used in very inappropriate and aggressive situations.