# He will cut away

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

# just as the fat is cut away

"just as a person cuts away the fat" 

# will burn it

"will burn the fat"

# to produce a sweet aroma for Yahweh

Yahweh being pleased with the sincere worshiper who offered the sacrifice is spoken of as if God were pleased with the aroma of the burning sacrifice.

# The priest will make atonement for the man

"The priest will atone for the man's sins" 

# he will be forgiven

"Yahweh will forgive the man's sins"