This paper provides a deep analysis for millimeter-wave device-to-device (mm-wave D2D) underlaid cellular networks to investigate how the performance of individual users or link percentiles under constraints are affected by the interaction between D2D and cellular communication modes integrated with the salient mm-wave features. Under a general Nakagami fading model, we derive the upper bounds for the$b$-moments of the conditional signal-to-interference-noise ratio (SINR) distributions for the two modes given the network realization, and further calculate the upper bounds of SINR meta distributions (MDs). Moreover, we extend the MD-based analysis to evaluate the fine-grained performance for the transmission effectiveness, through deriving the bounding results for the user-perceived rate MD and spatial rate capacity (SRC), the latter of which is defined as the effective density of users satisfying a given transmission rate requirement with a certain probability. Numerical results validate the tightness of the proposed bounds and reveal the different effects of the network configuration parameter associated with mm-wave on the link and network performances from the view of individual users.