If I want to ask someone to shut up right off the bat because I am tired of listening to his talktiveness, can I say something like "Shut up or I will block off your mouth".
I just want to know if "block off" can be used in such a situation. Thanks.

You could say it, but it is not at all idiomatic.

In addition, you would need to be careful who you say it to, or you might get a punch in the nose!Emotion: angry

I've heard of "knock your block off" to mean hit you in the head.

Don't say it to anyone you'd like to have a further conversation with, however.

It can also be used in a situation like, "she is so beautiful she just knocks your block off".

[edit or is that knock your socks off?]
Students: We have free audio pronunciation exercises.

If you want someone to stop talking, and you want to be extrememly offensive and threatening, you could say, "Shut your mouth or I'll shut it for you" or "Shut up or I'll shut you up." (I don't know anyone who would actually speak this way, except for a villain or a vicious thug in a TV show or movie.)
That's it; keep me in the loop.

When are we going to get together?
Students: Are you brave enough to let our tutors analyse your pronunciation?
Emotion: wink