Colorectal cancer, largely arising from precursor lesions called polyps, remains one of the leading causes of cancer-related death worldwide. Current clinical standards require the resection and histopathological analysis of polyps due to test accuracy and sensitivity of optical biopsy methods falling substantially below recommended levels. In this study, we design a novel capsule network architecture (D-Caps) to improve the viability of optical biopsy of colorectal polyps. Our proposed method introduces several technical novelties including a novel capsule architecture with a capsule-average pooling (CAP) method to improve efficiency in large-scale image classification. We demonstrate improved results over the previous state-of-the-art convolutional neural network (CNN) approach by as much as 43%. This work provides an important benchmark on the new Mayo Polyp dataset, a significantly more challenging and larger dataset than previous polyp studies, with results stratified across all available categories, imaging devices and modalities, and focus modes to promote future direction into AI-driven colorectal cancer screening systems. Code is publicly available at https://github.com/lalonderodney/D-Caps.