Millimeter wave (mmWave) communications are sensitive to blockage over radio propagation paths. The emerging paradigm of reconfigurable intelligent surface (RIS) has the potential to overcome this issue by its ability to arbitrarily reflect the incident signals toward desired directions. This paper proposes a Neyman-Pearson (NP) criterion-based blockage-aware algorithm to improve communication resilience against blockage in mobile mmWave multiple input multiple output (MIMO) systems. By virtue of this pragmatic blockage-aware technique, we further propose an outage-constrained beamforming design for downlink mmWave MIMO transmission to achieve outage probability minimization and achievable rate maximization. To minimize the outage probability, a robust RIS beamformer with variant beamwidth is designed to combat uncertain channel state information (CSI). For the rate maximization problem, an accelerated projected gradient descent (PGD) algorithm is developed to solve the computational challenge of high-dimensional RIS phase-shift matrix (PSM) optimization. Particularly, we leverage a subspace constraint to reduce the scope of the projection operation and formulate a new Nesterov momentum acceleration scheme to speed up the convergence process of PGD. Extensive experiments confirm the effectiveness of the proposed blockage-aware approach, and the proposed accelerated PGD algorithm outperforms a number of representative baseline algorithms in terms of the achievable rate.