Compressed sensing (CS)-based techniques have been widely applied in the grant-free non-orthogonal multiple access (NOMA) to a single-antenna base station (BS). In this paper, we consider the multi-antenna reception at the BS for uplink grant-free access for the massive machine type communication (mMTC) with limited channel resources. To enhance the overloading performance of the BS, we develop a general framework for the synergistic amalgamation of the spatial division multiple access (SDMA) technique with the CS-based grant-free NOMA. We derive a closed-form statistical beamforming and a dynamic beamforming scheme for the inter-cluster interference suppression when applying SDMA. Based on this, we further develop a joint adaptive beamforming and subspace pursuit (JABF-SP) algorithm for the multiuser detection and data recovery, with a novel sparsity level decision method without the accurate knowledge of the noise level. To further improve the data recovery performance, we propose an interference cancellation-based J-ABF-SP scheme (J-ABF-SP-IC) by using the initial signal estimates generated from the J-ABF-SP algorithm. Illustrative simulations verify the superior user detection and signal recovery performance of our proposed algorithms in comparison with existing CS-based grant-free NOMA techniques.