Low bit-precisions and their bit-slice sparsity have recently been studied to accelerate general matrix-multiplications (GEMM) during large-scale deep neural network (DNN) inferences. While the conventional symmetric quantization facilitates low-resolution processing with bit-slice sparsity for both weight and activation, its accuracy loss caused by the activation's asymmetric distributions cannot be acceptable, especially for large-scale DNNs. In efforts to mitigate this accuracy loss, recent studies have actively utilized asymmetric quantization for activations without requiring additional operations. However, the cutting-edge asymmetric quantization produces numerous nonzero slices that cannot be compressed and skipped by recent bit-slice GEMM accelerators, naturally consuming more processing energy to handle the quantized DNN models. To simultaneously achieve high accuracy and hardware efficiency for large-scale DNN inferences, this paper proposes an Asymmetrically-Quantized bit-Slice GEMM (AQS-GEMM) for the first time. In contrast to the previous bit-slice computing, which only skips operations of zero slices, the AQS-GEMM compresses frequent nonzero slices, generated by asymmetric quantization, and skips their operations. To increase the slice-level sparsity of activations, we also introduce two algorithm-hardware co-optimization methods: a zero-point manipulation and a distribution-based bit-slicing. To support the proposed AQS-GEMM and optimizations at the hardware-level, we newly introduce a DNN accelerator, Panacea, which efficiently handles sparse/dense workloads of the tiled AQS-GEMM to increase data reuse and utilization. Panacea supports a specialized dataflow and run-length encoding to maximize data reuse and minimize external memory accesses, significantly improving its hardware efficiency. Our benchmark evaluations show Panacea outperforms existing DNN accelerators.