The suspected green mamba was found on a ship that had docked in Aberdeen from west Africa last month.
The snake died after it was placed in a freezer by the animal charity after attempts to rehome it with specialist reptile keepers failed.
The snake was later identified as a harmless green tree snake.
Police Scotland said a complaint was under consideration.
Scottish SPCA Ch Supt Mike Flynn said: "We were called out after a green snake arrived in Aberdeen on a boat from Africa.
"The snake was thought to be a green mamba, one of the deadliest snakes in the world. The snake was taken by police escort to our Aberdeenshire animal rescue and rehoming centre.
"Sadly the snake, which staff genuinely believed to be a green mamba, had to be put to sleep after our attempts to rehome it to specialist reptile keepers were unsuccessful."
He added: "We could not keep the snake in our centre due to severe health and safety concerns, as the closest anti-venom is held in Bedford. Green mambas also require a Dangerous Wild Animal Licence which the society does not have.
"The safety of our staff and the public is paramount and as such the snake was placed in a freezer where it passed away.
"The Scottish SPCA is proud of its policy not put healthy animals to sleep. Animals are only put to sleep on veterinary advice if they are too ill or too aggressive to be rehomed, or where we are legally required to do so.
"The decision to euthanise the snake was not taken lightly. Unfortunately, the snake has since been identified as a harmless green tree snake. This has been an honest mistake on the society's part as we genuinely believed this was an extremely deadly snake."
The western green mamba feeds on small animals and rodents and is mainly found in the coastal tropical rainforests of western Africa.
Experts say its bite can be fatal in as little as 30 minutes.

Communication between two proteins is what triggers the cell tent to lose its shape and become unanchored, their research found.
This allows the cells to travel to other areas of the body.
The researchers said their findings could help prevent the spread of lung cancer.
Writing in the Journal of Clinical Investigation, researchers from York and the University of Texas describe how the communications centre of a cell - known as the Golgi apparatus - receives a signal from proteins which prompts the movement of membrane sacks inside it.
This movement alters the shape and surface of the cancer cell, allowing it to break free from its moorings and move around freely.
Dr Daniel Ungar, from the University of York's biology department, said it was apt to think of the cancer cell resembling a tent structure.
"It has fixed sides to hold its shape and is firmly anchored to the ground in order to secure its contents.
"In order to move the tent, we have to rearrange its contents and collapse its sides in order to lift it out of its anchored position and carry it away," he said.
He added that a similar process happens with cancer when it spreads - its outer edges are altered leaving it unanchored.
The study found that a protein called Zeb1 was critical to this process and the research team now want to look at how to target the protein without damaging healthy cells, in which the protein also exists.
The researchers only looked at lung cancer cells and do not know if the same process occurs in other cancers.
A complaint about the Scottish SPCA putting what was thought to be one of the world's most deadly snakes to sleep is being investigated by police.
[NEXT_CONCEPT]
Spreading lung cancer cells are like tents which have collapsed and are adrift in the wind, scientists from the University of York have discovered.