What should I do if some bird species killed on purpose?

What you can and may do.
What I do.

Annotate as dead - in the hopes that one day iNat will enable a personal option to ‘unsee dead obs’. That also keeps the data useful and searchable.
Mark as reviewed. (You could also skip the annotation if you prefer that way)

Feature request declined. 44 votes. 150 comments. You are not alone.

@tiwane 's response there

So we discussed this have decided not move forward with a specific way of handling observations of dead organisms or observations that include gory images. What we want to focus on instead is making better filters, including exclusion filters, in the user interface on Explore and Identify. Unfortunately, that won’t happen until Explore is rewritten. In the meantime, you can currently exclude annotations by editing the URL, see https://forum.inaturalist.org/t/how-to-use-inaturalists-search-urls-wiki-part-2-of-2/18792