The increasing prevalence rate of chronic wounds across the globe has negatively impacted the patients' lives and placed a burden on the healthcare system. With the advancement in artificial intelligence techniques, the wound assessment process is also moving towards automation, which will facilitate clinicians in monitoring the wound and prescribing suitable medication. Wound area measurement is important in assessing wounds and their healing progress; however, wound segmentation aids in measuring wound area. Because of the hazy wound boundaries, varied colorations, irregular shapes, and diverse wound attributes, accurate wound segmentation is challenging in medical imaging. Therefore, this paper presents SwishRes-U-Net (SRU-Net), a deep-learning framework for accurately segmenting chronic wounds, particularly diabetic foot ulcers. SRU-Net is based on dual UNets having encoders and decoders. To deal with the issue of limited data samples, pre-trained SwishResNet is utilized in the encoder1; however, the encoder2 is trained from scratch on the wound dataset. We also introduce spatial-channel squeeze-&-excitation (SC-S&E) blocks embedded in decoders and encoder2 modules. SC-S&E block extracts spatial and channel-wise relevant features that help accurately segment wound area. The effectiveness of the proposed model is evaluated utilizing two wound segmentation datasets: the AZH wound segmentation dataset and the foot ulcer segmentation (FUSeg) challenge dataset. SRU-Net has achieved 92.57% and 91.81% dice scores on AZH and FUSeg datasets. Moreover, cross-dataset validation is also conducted to assess the model's generalization potential. Quantitative and qualitative analysis of the obtained results reveal the efficacy of the proposed SRU-Net for the segmentation of chronic wound images. [ABSTRACT FROM AUTHOR]