Dich Bastard bring ich um!

English Translation

You bastard, I’ll kill you!

Surely that should be “du”? Is it not two separate clauses, as in English?

Ich bringe dich um, du Bastard!

No, the “dich” is the object to “umbringen”
Your sentence
“Ich bringe dich um” is perfect, just as
“Ich bringe dich um, du Bastard”.
Now you cam leave out the pronoun
“Ich bringe dich um, Bastard”
and finally get the “salutation” in front:
Dich, Bastard, bringe ich um.

Would be more fun to explain it with

“Dich, meine Geliebte, werde ich nie verlassen,”