Nottinghamshire PC Andrew Tideswell sent the messages to Samantha Goodwin, a former constable sacked for leaking information about a missing schoolgirl.
The force said the texts showed a lack of "respect and courtesy".
PC Tideswell said it was "thought policing" because they were on his private phone.
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A misconduct hearing at Nottinghamshire Police headquarters was told PC Tideswell's phone was seized when his then girlfriend's house was searched in an investigation into the leaking of information about Amber Peat.
Ms Goodwin has since been sacked for sending messages to friends about Amber's death.
Over two years, PC Tideswell, 38, sent messages which included calling a murder victim a "paedo gay boy",  a suspect a "muppet with autism", a man who attempted suicide a "numpty", and a victim of grooming a "bit of a slut".
Matthew Green, representing Nottinghamshire Police, said the messages "demonstrate an enormous lack of respect and courtesy and a terminal lack of awareness of how you should behave as a police officer."
PC Tideswell, an officer with 14 years' experience, based in Mansfield, said: "The messages were hermetically sealed within my phone and the relationship... They were never intended to get into the public arena.
"None are reflective of my day-to-day personality."
His representative told the hearing no confidential information was given out and spur-of-the-moment private comments made from one officer to another could not form the basis of misconduct.
Assistant Chief Constable Simon Torr said the officer had shown an "arrogant, dismissive and disdainful attitude".
Giving him a final written warning, Mr Torr said: "The comments in this case were absolutely unacceptable.
"It was so finely balanced that the good and potential for future good outweighs the bad.
"We are therefore prepared to give PC Tideswell the opportunity to demonstrate that he can serve the public."
A PC who sent homophobic and other "unacceptable" messages about suspects and crime victims to his girlfriend is being allowed to keep his job.