The incident happened around 3:20 Friday afternoon in the parking lot of the Walmart on the 1200 block of Centerville Road.
20-year-old Stephen Dunfee II and 19-year-old Devin Holt were arrested outside the store.
Authorities say a 35-year-old woman was walking to her car with a shopping cart when Dunfee grabbed her purse.
He then tried to run to the getaway car, which police say was being driven by Holt, but several Good Samaritans were able to stop him.
Holt sped off but another Good Samaritan jumped in and took down the license plate.
Dunfee and Holt were both taken into custody and face robbery charges.