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Magnetic Resonance cardiac diffusion tensor imaging (cDTI) and cardiac intravoxel incoherent motion imaging enables probing of in vivo myofiber architecture and myocardial perfusion surrogates. To study the impact of experimental parameters such as resolution, off-resonances and heart-rate variations, we propose a numerical open-source framework called MRXCAT-CDTI. It allows simulating diffusion and perfusion contrast for spin-echo (SE) and stimulated echo acquisition mode (STEAM) cDTI sequences. The Fourier encoder supports in-plane and/or through-slice off-resonance effects, as well as T2* effects during single-shot image encoding. Optional lesions are included to mimic ischemic and infarcted myocardial regions. MRXCAT-CDTI allows assessing realistic influences on data acquisition, and how these affect the data encoding process and subsequent data processing. As an example, heart-rate variations lead to differences in partial saturation and relaxation of magnetization that end up in errors of 9 to 30% for cDTI angle metrics if not accounted for. For SE echo-planar cDTI, in-plane off-resonance effects more adversely affect cDTI metrics compared to through-slice off-resonances. With this work we propose an open-source MRXCAT-CDTI numerical simulation framework that offers realistic image encoding effects found in cardiac diffusion and perfusion data to systematically study influences of data encoding, reconstruction, and post-processing to promote reproducible research.