Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for realizing future wireless systems. In this paper, we propose an ISAC processing framework relying on millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Specifically, we provide a compressed sampling (CS) perspective to facilitate ISAC processing, which can not only recover the high-dimensional channel state information or/and radar imaging information, but also significantly reduce pilot overhead. First, an energy-efficient widely spaced array (WSA) architecture is tailored for the radar receiver, which enhances the angular resolution of radar sensing at the cost of angular ambiguity. Then, we propose an ISAC frame structure for time-varying ISAC systems considering different timescales. The pilot waveforms are judiciously designed by taking into account both CS theories and hardware constraints induced by hybrid beamforming (HBF) architecture. Next, we design the dedicated dictionary for WSA that serves as a building block for formulating the ISAC processing as sparse signal recovery problems. The orthogonal matching pursuit with support refinement (OMP-SR) algorithm is proposed to effectively solve the problems in the existence of the angular ambiguity. We also provide a framework for estimating the Doppler frequencies during payload data transmission to guarantee communication performances. Simulation results demonstrate the good performances of both communications and radar sensing under the proposed ISAC framework.