Source-Free Domain Adaptation (SFDA) is emerging as a compelling solution for medical image segmentation under privacy constraints, yet current approaches often ignore sample difficulty and struggle with noisy supervision under domain shift. We present a new SFDA framework that leverages Hard Sample Selection and Denoised Patch Mixing to progressively align target distributions. First, unlabeled images are partitioned into reliable and unreliable subsets through entropy-similarity analysis, allowing adaptation to start from easy samples and gradually incorporate harder ones. Next, pseudo-labels are refined via Monte Carlo-based denoising masks, which suppress unreliable pixels and stabilize training. Finally, intra- and inter-domain objectives mix patches between subsets, transferring reliable semantics while mitigating noise. Experiments on benchmark datasets show consistent gains over prior SFDA and UDA methods, delivering more accurate boundary delineation and achieving state-of-the-art Dice and ASSD scores. Our study highlights the importance of progressive adaptation and denoised supervision for robust segmentation under domain shift.