The puppy, a 10-month-old Cavapoochon, was taken from a house in Othery, near Bridgwater, between 9.30am and 11am on Wednesday, March 24.
It was later found dead by a member of the public on Beer Drove, off the A372.
PC Claire Allan said: “This is an extremely upsetting case for all pet owners and I’d like to reassure people we’re working closely with the RSPCA to identify those responsible.
“House to house enquiries have been carried out and we’ll also be reviewing CCTV from the local area as part of our inquiry.
“Were you in the area around the time of the incident? Did you see anything suspicious?
“If you have any information which could help us please contact us on 101 giving the call handler reference 5221063875.”
Alternatively, you can contact the independent charity Crimestoppers 100 per cent anonymously on 0800 555 111 or via their Anonymous Online Form.