Tenderization based on papain and microwave vacuum drying and puffing (MVDP) as well as adequate processing conditions enabled expansion of slices of the raw meat tissue. The main aim of the study was to use the response surface method and find the conditions of puffing that could maximize the expansion of meat during MVDP. The bound was set on the expansion: the most expanded puffings should be of good quality, including a desirable porous structure. The best combination of values of the MVDP process conditions (e.g., the initial moisture content in meat slices, microwave energy, and the vacuum absolute pressure) was found during experiments using the central composite design. The volume of slices puffed under these conditions was 1.60–1.78 times greater than the volume of slices before MVDP, and the sensory quality index remained acceptable. The research showed that pretreatment reduced the hardness of sample by over 25% and increased its crispiness, which was confirmed in cryo-scanning electron microscopy images.