We consider link scheduling in wireless networks for emptying the queues at the transmitters in minimum time, with time constraints, or deadlines, for one or multiple individual links. We formulate the minimum-time scheduling problem with deadlines (MTSD) mathematically and derive the optimal activation order of the link sets in a schedule solution. Theoretical results are obtained, showing that the MTSD can be treated as the conventional minimum-time scheduling problem by "absorbing" the deadline constraints into the rate region where the scheduling problem is defined. By this approach, optimality characterization and geometric interpretation for the MTSD are provided. Furthermore, we extend the results to the MTSD in a general form that accommodates an arbitrary rate region.