With the increasing popularity of robotics in industrial control and autonomous driving, deep reinforcement learning (DRL) raises the attention of various fields. However, DRL computation on the modern powerful GPU platform is still inefficient due to its heterogeneous workloads and interleaved execution paradigm. To this end, we propose GMI-DRL, a systematic design to accelerate multi-GPU DRL via GPU spatial multiplexing. We introduce a novel design of resource-adjustable GPU multiplexing instances (GMIs) to match the actual needs of DRL tasks, an adaptive GMI management strategy to simultaneously achieve high GPU utilization and computation throughput, and a highly efficient inter-GMI communication support to meet the demands of various DRL communication patterns. Comprehensive experiments reveal that GMI-DRL outperforms state-of-the-art NVIDIA Isaac Gym with NCCL (up to 2.81X) and Horovod (up to 2.34X) support in training throughput on the latest DGX-A100 platform. Our work provides an initial user experience with GPU spatial multiplexing in processing heterogeneous workloads with a mixture of computation and communication.