Matthew Sanchez was reassigned after the incident in New Mexico on 23 June, but quit on Tuesday after a recording of the call was released.
He was dealing with a friend of Jaydon Chavez-Silver, 17, who had been shot in a drive-by shooting in Albuquerque.
Officials said an ambulance was sent to the scene but Chavez-Silver later died.
In the recording the panicked caller, 17-year-old Esperanza Quintero, is heard swearing at Sanchez after he repeatedly asks whether Chavez-Silver is breathing.
During the call, Mr Sanchez asks the young woman if Chavez-Silver is breathing, to which she replies: "Barely!"
She is then heard encouraging her friend before Mr Sanchez asks the same question again.
An exasperated Ms Quintero responds using an expletive to which Mr Sanchez says: "OK, you know what ma'am? You can deal with it yourself. I am not going to deal with this, OK?"
From the tape it appears that Mr Sanchez hangs up as the caller says: "No, my friend is dying".
Earlier this week, Ms Quintero told the local KOAT-TV network: "It was his job. I don't understand why he would have hung up."
A statement released on Tuesday evening from the office of Albuquerque's chief administrative officer said Mr Sanchez has resigned from the local fire department.
He had worked there for 10 years, originally as a firefighter. He had been assigned to the emergency dispatch centre for nearly three and a half years, officials said.
Albuquerque police have made no arrests over Chavez-Silver's death and have not named any suspects.

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At 63-63, Robertson took the first frame with a respotted black but Carter took the second with a 94 break.
Carter won the third frame to go 2-1 up but Robertson fought back with a break of 43 and 57 to take a 3-2 lead.
However, Carter came from behind to seize victory, as he won three straight frames including an 84 break.
He will face off against Trump, who beat Ronnie O'Sullivan on Wednesday, in Friday's semi-final.
Semi-finals
Judd Trump v Ali Carter
Mark Selby/Marco Fu v Ding Junhui/Anthony Hamilton
Quarter-finals
Mark Selby v Marco Fu
Ding Junhui v Anthony Hamilton
Neil Robertson 3-5 Ali Carter
Ronnie O'Sullivan 3-5 Judd Trump
Round one
Stuart Bingham 1-5 Anthony Hamilton
Ronnie O'Sullivan 5-1 Liang Wenbo
Mark Selby 5-4 Ryan Day
Marco Fu 5-1 Anthony McGill
Barry Hawkins 0-5 Neil Robertson
Judd Trump 5-2 Mark King
Ding Junhui 5-4 John Higgins
Ali Carter 5-4 Shaun Murphy
A 911 dispatcher in the US has resigned after telling a frantic caller who was trying to save the life of a shooting victim to "deal with it yourself".
[NEXT_CONCEPT]
Ali Carter beat Neil Robertson 5-3 in the Players Championship quarter-final in Llandudno, to set up a semi-final tie against Judd Trump on Friday.