The merge of mobile edge computing (MEC) and millimeter-wave (mmWave) communications will hopefully enable the fast access for computational resources, where these two technologies can benefit from each other's potentials. However, the high susceptibility to blocking in mmWave networks imposes crucial challenges for further development of mmWave-MEC vision. In this paper, a novel intelligent reflecting surface (IRS) assisted mmWave-MEC scheme is proposed to overcome the disruptive effect caused by blockage events. In this context, we investigate new methods to minimize mobile power for a multi-user mmWave-MEC system, thus efficiently orchestrating the uplink mobile power resources for latency-constrained computation offloading. In particular, the mobile power is optimized by joint design of individual device power, multi-user detection matrix and passive beamforming. To tackle this issue, we develop an alternating optimization framework so that the joint optimization can be decomposed into tractable subproblems. First, we provide closed-form expressions for the update of powers and multi-user detection vectors in each iteration step. Then, we reformulate the passive beamforming problem. To cater for large-scale IRS scenario, we propose two efficient algorithms including complex circle manifold optimization (CCMO) method and sum-of-inverse minimization (SIMin) fraction transform based alternating direction method of multipliers (ADMM) method. Finally, numerical results corroborate the merits of our proposed IRS assisted mmWave-MEC scheme, and demonstrate the feasibility and effectiveness of our algorithms.