A lunatic hacked off his Bronx neighbor’s hand and then fatally slit her throat with a machete in an unprovoked attack on Sunday, according to police sources.

Angel Feliz-Volquez, 25, ambushed and butchered Carmen Torres-Gonzalez, 59, as she chatted with her mother’s home health-care aide outside their fifth-floor apartment in the Mott Haven Houses, law-enforcement sources said.

The victim was found lying in a pool of blood in the hallway just after 4 p.m., the sources said.

Her right hand had been chopped off completely, her left hand was partially severed and she had suffered cuts to her throat, cheek and shoulder.

Cops nabbed Feliz-Volquez a short time later in his apartment, which is in the same building — and on the same floor — as the victim’s.

Officers recovered the machete in the stairwell.

Charges against Feliz-Volquez — whom neighbors described as “the mental guy” — are pending, according to sources.

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