There are mainly two factors, multipath effect and strong background noise, affecting the performance of underwater weak acoustic signal detection. In this paper, to improve the performance, we propose a joint detection approach for underwater weak acoustic signal by combining the approaches of Passive Time Reversal (PTR) and Stochastic Resonance (SR). By calculating the input and output signal-to-noise ratios (SNR) theoretically, it's found that the proposed PTR-SR approach could improve the SNR of received signal, which is obtained by utilizing the multipath propagation channel and background noise simultaneously. Further, we propose a strategy to properly setting the free amplitude parameter A_sr to optimize the SNR gain. Based on the Neyman-Pearson criterion, simulation results also highlight the performance of the proposed joint detection approach over single PTR approach and SR approach, especially in the circumstance of low SNR.