If people are sending you threats, block them. Report them if necessary.

As Ace said. If people are threatening you with actual harm, that's a reportable offense, and in many states of the US, a legit crime. I may have my reservations about some folks' behaviors, but harassment to that extent is, in fact, unacceptable and against the TOS of almost all websites and chat clients. If you're being harassed this badly, definitely use the proper channels to fight back. As for public opinion... That can be a slippery slope. I won't get into that one too much, but if it's grown this bad, maybe reflect on two things... The nature of those who are being problematic, and on your own conduct. That is my two cents, take or leave...

I've reported someone for literal death threats that include drawing themself murdering me and Twitter shot back with "the reported tweets are not against our TOS."

Cite their TOS against them. Isn't graphic depiction of death against their TOS?

Tried that. Twitter evidently does not reply back after rejecting a report.

File a new one, or have a friend do so.

That has been tried as well. The latter, that is.

Not sure what to suggest at that point. Typically, my saving grace when others try to spread negative rumors is simply that I try to be as good a person as I reasonably can. There's always going to be some ass who will spread negative rumors... Just try to build up a positive reputation despite them?