# He will cut away

Here "He" refers to the person offering the sacrifice.

# just as the fat of the lamb is cut away

"just as a person cuts away the fat of the lamb" 

# the priest will burn it

"the priest will burn the fat"

# offerings of Yahweh made by fire

"burnt offerings for Yahweh" 

# will make atonement for him for the sin he has committed

"will atone for the sin the person committed"

# the man will be forgiven

"Yahweh will forgive the man's sins"