Tell me, '' why I shouldn't beheaded you? " name the subordinate clause.
I'm going to correct your sentence first and them explain it. If I correct it incorrectly, please comment.
Tell me why I shouldn't behead you.
Regarding the corrections:
Proper tense of "should" clauses.
should (not) behead -> present conditional (Type 1 from reference below)
should (not) have beheaded -> past conditional (Type 3 below)
Please reference Type 1 and Type 3 conditionals here. That page is primarily about "if" but it applies to "should" and the other conditional expressions.
The format you used with a comma and quotation is only used for direct quotes. When written that way, it indicates that the quoted words are actually spoken as a stand-alone sentence. Therefore, the contents of the quotation should be a complete sentence. For example:
He said, "Where should I go?"
If I were told that what you wrote is definitely correct as written, it would indicate that the speaker wanted the listener to actually say "Why I shouldn't beheaded you?" However, such a commend would usually start with "Say" rather than "Tell me"
The correct way to write your sentence is using "embedded question" format (no comma, quotation marks, or question mark).
Now to answer your question, the subordinate clause is:
why I shouldn't behead you.
The above is a clause (a sentence piece that includes both subject and predicate (verb)) however it cannot stand alone because it is a conditional clause.