This paper proposes an ultra-low power, mixed-bit-width sparse convolutional neural network (CNN) accelerator to accelerate ventricular arrhythmia (VA) detection. The chip achieves 50% sparsity in a quantized 1D CNN using a sparse processing element (SPE) architecture. Measurement on the prototype chip TSMC 40nm CMOS low-power (LP) process for the VA classification task demonstrates that it consumes 10.60 $\mu$W of power while achieving a performance of 150 GOPS and a diagnostic accuracy of 99.95%. The computation power density is only 0.57 $\mu$W/mm$^2$, which is 14.23X smaller than state-of-the-art works, making it highly suitable for implantable and wearable medical devices.