A woman whose decomposing torso was found in a garbage bag by sanitation workers picking up trash at a Queens park near JFK Airport was coldly chopped into pieces — with her head and limbs methodically sliced off — according to police.

After her death, “a knife was used to cut through the soft tissue, and a saw was used to cut through the bone,” NYPD Chief of Detectives Joseph Kenny said Thursday of the victim.

The victim also “had several unique and identifying tattoos,” that could provide clues to her identity, Kenny added.

Cops are continuing to scour open missing persons cases for potential leads.

Department of Sanitation workers doing roadside cleanup called police after finding the garbage bag containing the woman’s remains near 149th Ave. and Brookville Blvd. on the edge of I

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