Recently, our proposed speaker extraction model, WASE (learning When to Attend for Speaker Extraction) yielded superior performance over the prior state-of-the-art methods by explicitly modeling onset clue and regarding it as important guidance in speaker extraction tasks. However, it still remains challenging when it comes to the deployments on the resource-constrained devices, where the model must be tiny and fast to perform inference with minimal budget in CPU and memory while keeping the speaker extraction performance. In this work, we utilize model compression techniques to alleviate the problem and propose a lightweight speaker extraction model, TinyWASE, which aims to run on resource-constrained devices. Specifically, we mainly investigate the grouping effects of quantization-aware training and knowledge distillation techniques in the speaker extraction task and propose Distillation-aware Quantization. Experiments on WSJ0-2mix dataset show that our proposed model can achieve comparable performance as the full-precision model while reducing the model size using ultra-low bits (e.g. 3 bits), obtaining 8.97x compression ratio and 2.15 MB model size. We further show that TinyWASE can combine with other model compression techniques, such as parameter sharing, to achieve compression ratio as high as 23.81 with limited performance degradation. Our code is available at https://github.com/aispeech-lab/TinyWASE.