The CDC haven't released any national statistics on suicide, etc. But there is a file that contains "All Cause" mortality and "Natural Cause" mortality, so I subtracted the two and got what should be the count for non-natural causes. That would include homicide, suicide, accidents, poisonings, overdoses.
Here is the graph I got: https://imgur.com/N4lSSam
The drop-off at the end is because of reporting lag. There is more of a drop-off with these than other causes, presumably because producing a final death certificate takes more time on average (forensic autopsies, toxicology testing, etc.).
Through week 35, there were about 13,000 more non-natural cause deaths in 2020 over 2019.
By comparison, the number of excess deaths through week 35 was 258,846. That implies that 95% of the excess deaths were natural causes.
Here are some spreadsheets I've made from CDC data:
[1] Weekly counts of deaths by select causes
[1] https://docs.google.com/spreadsheets/d/1G31ODc4eVgzg7etmcCV5...
[2] US Deaths by Week and Year
[2] https://docs.google.com/spreadsheets/d/1qucznpabG1aUz0GSiDbi...
[3] U.S. Excess deaths by age
[3] https://docs.google.com/spreadsheets/d/1rcGoWRsNxS_zJQ3pJtbW...