Ha Rav, If a man finishes a Masechet or a book of Tanach does is it a mitzvah to do a siyum? What mitzvah is it in the 613 mitzvot?
Yes it is a mitzva to make a siyum when a person finishes a mesechet or a sefer of Nach. the reason for this is in order to sow appreciation for the opportunity to learn Hashem’s Torah, (see Introduction to the sefer “Yoma Tava L’rabonon”, who brings a number of reasons for this).
The term “mitzva” here, is not referring to one of the actual 613 mitzvos written in the Torah, rather it is a term used, for positive things that chazal knew Hashem wants us to do. Here are a few examples where this term is used, see O:CH 224-9, 293-1, 167-6.