Nearly 3,000 offenders who have committed "minor" crimes including shop theft, assault and drug offences have been given formal cautions by South Australian Police officers under a new initiative.

SA Police announced the national-first program, adult cautioning for low-level criminal offending, was being trialled from August last year and began statewide in December.

Since then 2,044 cautions have been issued instead of matter being taken to court.

The system is similar to the juvenile caution program which has run in the state for 25 years.

Examples of cases where a caution has been issued included a 86-year-old who stole sausage and mints valued at $7.85 only weeks after his wife died, a 48-year-old beggar and a 76-year-old man who removed clothing from a charity bin.

The program, which was trialled in Whyalla and Eastern Adelaide last year, is applied when there is a reasonable prospect of conviction, the matter is minor, is approved by a sergeant and a caution is considered proportional to the offence.

Factors considered include the offender's history, the opinion of the victim of crime, and seriousness of the offence.

Assistant Commissioner Phil Newitt said the program recognised that "not all offences we detect should necessarily go to court".

"It allows our officers to apply common sense to how we manage the outcome of an investigation.

"It is very much focused on proportionality in terms of the offences and all the accompanying circumstances."

Cautions cannot be issued for any aggravated offences, any offence under the serious and organised crime definitions, an offence involving violence, stalking or harassment against a family member, sexual offence or drug offence, except for smoking or consuming cannabis.