An animal welfare charity said the figures highlight how too many people are buying dogs as pets when they cannot afford them and then later abandoning them.
READ MORE: Power cut hits 170 Doncaster homes
Dr Samantha Gaines, a dog welfare expert for the Royal Society for the Prevention of Cruelty to Animals, said people should think long and hard about the cost of having a dog before going through with the purchase.
She said: "It's really sad that so many stray dogs are euthanised each year and highlights a real problem in this country with pet buying habits and ownership.
Man seriously ill in hospital as Doncaster city centre street cordoned off after assault
Hosepipe ban for Doncaster as Yorkshire Water introduces drought restrictions
Major Doncaster bridge will be closed for a whole month for essential maintenance
Watch: Ex-Red Arrows pilots create heart over Doncaster in surprise aerobatic display
Family's plea after teenager with mental health issues goes missing in Doncaster
"The RSPCA would urge anyone thinking of getting a dog to first consider what is involved. It's important the whole family is prepared for the commitment - both financial and time - before bringing one home."
She added many strays end up in the council dog pound because their owners have not microchipped them - which is now a legal requirement.
Dr Gaines said: "We would urge all dog owners to get their pets chipped so more dogs can be returned home successfully, which would help cut down on the numbers that end up in pounds and rescue centres."
READ MORE: Broken track causes disruption for train users in South YorkshireThe figures - revealed using the Freedom of Information Act - showed 1638 dogs had been impounded by the council between 2014 and 2016.
A total of 197 were destroyed.
The council said there is a "very strict ethical code around euthanasia" and dogs are only put down in three circumstances and only as a last resort. This is if the dog would pose a risk to people, on the advice of a vet for medical purposes or if it is an illegal breed.
In addition, the number of strays impounded has also steadily decreased, dropping from 660 in 2014 to 450 in 2016. The euthanasia rate has also reduced in the same time frame from 87 to 40.
Concerned members of the public also called for more action to tackle the issue and took to Facebook to voice their concerns.
Sarah Smith posted: "I do''t agree with putting any dog to sleep. Stop breeding all these pedigrees that end up with health issues and go to an animal shelter for your dog."
READ MORE: Doncaster woman threatened with knife and screwdriver before being punched in terrifying robberyDave Wilkinson, assistant director of traded services and assets at Doncaster Council, said: “Our council dog wardens work very closely with kennel providers to find suitable homes for stray dogs, and we are successful in the vast majority of cases.
“To stop dogs from becoming strays, all owners are required to microchip their dogs and ensure the details are up to date. We also ask people to always think carefully before bringing a dog in to their family, and also to consider rehoming one of Doncaster’s stray dogs.”