The Specific Heat Capacity of Love definitely fits the description
http://www.mangago.zone/read-manga/the_specific_heat_capacity_of_love/
Also, Till Dawn is a very good one
http://www.mangago.zone/read-manga/till_dawn/
"Girl may kill" is sad. (Sorry I don't read a lot of sad stuff.)
http://www.mangago.zone/read-manga/deep_love_pao_no_monogatari/
This and the other deep love stories are a whole other level of sad. Heartbreaking enough to hurt your very soul
oyasumi punpun. it bored me to death though
http://www.mangago.zone/read-manga/oyasumi_punpun/
I want the saddest manga you've read. I feel like crap rn so what better way than just read sad, depressive stories that'll make me cry? Yaoi, Shoujo, Romance/Josei, Shounen, etc etc.