In order to ease the white pollution problem, biodegradable packaging materials are highly demanded. In this work, the biodegradable poly (butylene adipate-co-terephthalate)/MXene (PBAT/Ti3C2TX) composite casting films were fabricated by melt mixing. Then, the obtained PBAT/Ti3C2TX composite casting films were biaxially stretched at different stretching ratios so as to reduce the water vapor permeability rate (WVPR) and oxygen transmission rate (OTR). It was expected that the combination of Ti3C2TX nanosheets and biaxial stretching could improve the water vapor and oxygen barrier performance of PBAT films. The scanning electron microscope (SEM) observation showed that the Ti3C2TX nanosheets had good compatibility with the PBAT matrix. The presence of Ti3C2TX acted as a nucleating agent to promote the crystallinity when the content was lower than 2 wt%. The mechanical tests showed that the incorporation of 1.0 wt% Ti3C2TX improved the tensile stress, elongation at break, and Young’s modulus of the PBAT/Ti3C2TX nanocomposite simultaneously, as compared with those of pure PBAT. The mechanical dynamical tests showed that the presence of Ti3C2TX significantly improved the storage modulus of the PBAT nanocomposite in a glassy state. Compared with pure PBAT, PBAT-1.0 with 1.0 wt% Ti3C2TX exhibited the lowest OTR of 782 cc/m2·day and 10.2 g/m2·day. The enhancement in gas barrier properties can be attributed to the presence of Ti3C2TX nanosheets, which can increase the effective diffusion path length for gases. With the biaxial stretching, the OTR and WVPR of PBAT-1.0 were further reduced to 732 cc/m2·day and 6.5 g/m2·day, respectively. The PBAT composite films with enhanced water vapor and water barrier performance exhibit a potential application in green packaging.