Deep neural networks (DNNs) are known for their inability to utilize underlying hardware resources due to hardware susceptibility to sparse activations and weights. Even in finer granularities, many of the non-zero values hold a portion of zero-valued bits that may cause inefficiencies when executed on hardware. Inspired by conventional CPU simultaneous multithreading (SMT) that increases computer resource utilization by sharing them across several threads, we propose non-blocking SMT (NB-SMT) designated for DNN accelerators. Like conventional SMT, NB-SMT shares hardware resources among several execution flows. Yet, unlike SMT, NB-SMT is non-blocking, as it handles structural hazards by exploiting the algorithmic resiliency of DNNs. Instead of opportunistically dispatching instructions while they wait in a reservation station for available hardware, NB-SMT temporarily reduces the computation precision to accommodate all threads at once, enabling a non-blocking operation. We demonstrate NB-SMT applicability using SySMT, an NB-SMT-enabled output-stationary systolic array (OS-SA). Compared with a conventional OS-SA, a 2-threaded SySMT consumes 1.4x the area and delivers 2x speedup with 33% energy savings and less than 1% accuracy degradation of state-of-the-art CNNs with ImageNet. A 4-threaded SySMT consumes 2.5x the area and delivers, for example, 3.4x speedup and 39% energy savings with 1% accuracy degradation of 40%-pruned ResNet-18.