Millimeter-wave (mmWave) communications provide access to spectra with bandwidths and in abundance. However, the high susceptibility of mmWave to blockage imposes crucial challenges, especially to low-latency services. In this paper, a novel intelligent reflecting surface (IRS) assisted mmWave scheme is proposed to overcome the impact of blockage. New methods are developed to minimize the user power for a multi-user mmWave system by jointly optimizing individual device power, multi-user detection matrix and passive beamforming, subject to delay requirements. An alternating optimization framework is delivered so that the joint optimization problem can be decomposed into three subproblems iteratively optimized till convergence. In particular, closed-form expressions are devised for the update of the powers and multi-user detection vectors. The configuration of the IRS is formulated as a sum-of-inverse minimization (SIMin) fractional programming problem and solved by developing a new solution based on the alternating direction method of multipliers (ADMM). The configuration is also interpreted as a latency residual maximization problem, and solved efficiently by designing a new complex circle manifold optimization (CCMO) method. Numerical results corroborate the feasibility and effectiveness of our algorithms in terms of power saving, as compared with an existing semidefinite relaxation technique.