We present a safety-critical finite-time control framework for sampled-data multi-robot system coordination. We formally define and construct a finite-time discrete control Lyapunov function (FT-DCLF) and derive sufficient conditions that ensure convergence within a preset number of sampling steps, thereby enhancing both applicability and convergence speed. In parallel, we improve upon a discrete control barrier function (DCBF) constraint. This constraint addresses the continuous-discrete mismatch (“safety gap”) and ensures all-time safety, while mitigating deadlock and resolving performance-safety conflicts that are common in conventional DCBFs for obstacle avoidance. Both components, along with input bounds, are integrated into a single quadratically constrained quadratic program (QCQP), augmented with feasibility-aiding slack variables for real-time implementation. Simulation results demonstrate that the proposed method outperforms conventional DCLF-DCBF approaches.