This paper thoroughly investigates the performance of short-packet communications over cascaded fading channels that have a variety of applications in mobile-to-mobile (M2M) communications. By considering the wide occurrence of the correlation among cascaded fading processes, cascaded Nakagami-m channel model with general correlation is adopted. However, the presence of channel correlation poses significant challenges on the analysis of block error rate (BLER), which is the most fundamental performance metric in short-packet communications. For tractability, Mellin transform is first invoked to derive the BLER in terms of the representation of infinite summation. This result then enables the asymptotic analysis of BLER with useful insights, including the diversity order, the negative impact of correlation and the extension to infinite blocklength regime. Furthermore, to implement the infinite series representation of BLER, an effective truncation approach is proposed with controllable calculation accuracy. More importantly, our analytical results lay the foundation for the optimal system design. In the end, extensive Monte Carlo simulations verify our analysis.