Alec Bedford later showed a video of the incident to colleagues at Daventry Police Station.
A misconduct hearing in Northamptonshire concluded Special Sgt Bedford had been guilty of misconduct but not gross misconduct.
The officer, aged 26, did not attend the hearing.
For more on this and other stories, visit BBC Local Live: Northamptonshire
Sgt Bedford had been called to a house in Daventry in July 2015.
A 90-year-old man had refused to go to the police station after being arrested.
The man, referred to at the hearing as JA, had been accused of threatening behaviour towards a neighbour and of pulling his wife - JMA - by the hair two weeks previously.
The hearing heard Sgt Bedford had adopted a "confrontational approach".
At one stage he had bodily moved JMA across the room and had then pushed her in to a chair. JMA had scratched his arm and he decided to arrest her.
David Ring, a solicitor acting for the police force, said Sgt Bedford had acted unprofessionally by shouting at and "roughly handling" JMA.
JA was eventually taken to Daventry Police Station. His wife was given bail.
Sgt Bedford later showed video of the arrest to colleagues at Daventry Police Station.
Mr Ring said the officer had "behaved unprofessionally by laughing" and his actions constituted "a very complacent attitude to confidentiality."
Sgt Bedford pleaded guilty to charges relating to the use of excessive force, failing to act with courtesy and deliberately breaching confidentiality.
The misconduct panel's independent chairman, Geoffrey Payne, said: "This was a deeply disturbing and entirely unacceptable matter."
A part-time volunteer police sergeant who pushed an 87-year-old woman and shouted in her face has been given a final written warning.