A CCTV camera recording shows the life-saving device being removed from its container on the shop's wall at around 04:20 BST.
A suspect, believed to be male, is then seen throwing the device onto the Rossdowney Road.
The £1,500 defibrillator was bought by the local community after a fundraising campaign. It was installed in June.
The equipment was smashed to pieces, said Richard Campbell, manager of Curry's Spar shop in Church Meadow.
"It's life-saving equipment, accessible 365 days a year, it doesn't require any training and it's free to use," said Mr Campbell.
"He's taken it in his hand, launched it across the road, smashed it and destroyed it - £1,500 of life-saving equipment in pieces.
"We've been fundraising for about 12 months and we've only had it installed for two months. It took a lot of effort and time to get it installed," he added.
"The local people in this town, customers, that's who raised the money, and they are disgusted and so are we."
Police in Derry have appealed for witnesses to contact them.
Insp Gregory Smyth said: "This defibrillator was installed for the whole community to use in the case of an emergency and it is very disappointing that someone would want to damage this important piece of life saving equipment."
Staff at a shop in Londonderry have said they are "disgusted" after a defibrillator was vandalised on Sunday.