Yes, there would be a separate registers for births, marriages and burials (but possibly within the same book). Unfortunately, in Scotland, burials were not recorded often, and most records contain little information.
Sometimes you can find in the parish accounts, mention of someone’s death through the payment of a mortcloth.
If it is true that Alex Mitchell died in 1833, then I could find no record of a possible burial anywhere in Angus. There may be a gravestone to be found in a local churchyard.
I have not seen the full baptism record for James, but I would be somewhat suspicious that the father Alexander may not have died, but was recorded that way to help Ann Orchardson and the baby look more “respectable”.