I feel like censoring it would be unethical, while refusing to host it would simply be poor form.

Livecasting of own suicide: freedom of expression + freedom to make choices with regard to own life.

Edit: This is not to imply that Tumblr is not entitled to do whatever they damn please with their own website. But, should someone build a website specifically for livecasting suicides I would very much disagree with its censorship.

I consider suicide extremely sad, and would not feel particularly inclined to watch the video. Why are we even thinking about censorship in this hypothetical scenario? What good would censoring the video do?

Put a warning on it saying that it's NSFL, maybe run a free banner ad next to it for a suicide prevention hotline. Those things are reasonable, productive responses. Censorship of the video would be as symbolic as waving a flag, and about as useful.

Promoting suicide ≠ snuff films