Both “Je ne sais pas quoi dire” and “Je ne sais quoi dire” are correct translations for “I don’t know what to say”. With most verbs, skipping the “pas” sounds dated, but with “savoir”, not so much; still, the version with the “pas” probably remains more usual in everyday conversation.

However, the English “je ne sais quoi” (no “pas”!) actually comes from the French expression “un je ne sais quoi“, used as a noun. It has the same meaning in English as it does in French: something that you can’t exactly point out.

The negation is entirely expressed by the “ne”.

Pas, or in classical French point are just there to insist: pas même d’un pas, pas même d’un point — that is “not at all”.

Compare:

• je ne sais … = I don’t know …
• je ne sais pas / point … = I don’t know in the least …
• je ne sais pas du tout … = I don’t know at all …
• je ne sais guère … = I don’t know much about …

“Pas” is very usual, but in fact useless; the worst is the childish “J’sais pas”, where the negation is not expressed.

Pitfall:
“Je crains qu’il ne vienne” = “I am afraid that he could come” (and not: he could not come); it comes from a strange Latin turn of phrase “timeo ne veniat“.

In "Je ne sais quoi," quoi is an adequate closer for "ne." The sentence means "I don’t know anything."

It is just a bit weaker than "Je ne sais rien." (I know nothing.) Here, rien closes the negative.

In either case, you do not need the "pas," which would be redundant.

This post has more information on negatives