A K-tier heterogeneous mmWave uplink cellular network with clustered user equipments (UEs) is considered in this paper. In particular, UEs are assumed to be clustered around small-cell base stations (BSs) according to a Gaussian distribution, leading to the Thomas cluster process based modeling. Specific and practical line-of-sight (LOS) and non-line-of-sight (NLOS) models are adopted with different parameters for different tiers. The probability density functions (PDFs) and complementary cumulative distribution functions (CCDFs) of different distances from UEs to BSs are characterized. Coupled association strategy and largest long-term averaged biased received power criterion are considered, and general expressions for association probabilities are provided. Following the identification of the association probabilities, the Laplace transforms of the inter-cell interference and the intra-cluster interference are characterized. Using tools from stochastic geometry, general expressions of the SINR coverage probability are provided. As extensions, fractional power control is incorporated into the analysis, tractable closed-form expressions are provided for special cases, and average ergodic spectral efficiency is analyzed. Via numerical and simulation results, analytical characterizations are confirmed and the impact of key system and network parameters on the performance is identified.