In order to clarify the mechanism of influence of independent variables in terms of microwave power, vacuum degree, initial moisture content, and puffing time on the objective indexes, in terms of moisture ratio and expansion ratio, a series of single-factor experiments was performed during microwave vacuum puffing of raspberry leathers. The results showed that microwave power, vacuum, and initial moisture content had a significant influence on the dehydration and texture quality of raspberry snacks in terms of expansion ratio, hardness, and porosity. The change in both moisture content and volume obeyed a sigmoid function as microwave power, vacuum pressure, and initial moisture content, respectively. Both microwave power and initial moisture content had a positive influence on the puffing kinetics up to a certain value followed by negative trends, with the exception of vacuum pressure in the selected range of 15–45 kPa which was insignificant. Texture evolution, including hardness and porosity index processes, has three distinct stages during microwave vacuum puffing of raspberry leathers. But the change in temperature of raspberry leather lags behind that in the texture of hardness and porosity. Raspberry snacks with a high expansion ratio may be obtained under the following conditions: microwave intensity 28 Wg−1, vacuum pressure 30 kPa, and initial moisture content 20.0% (wb).