In this contribution, we demonstrate a hyperspectral mid-infrared (MIR) microscope based on multidimensional single-pixel imaging (SPI). The microscope employs a high brightness MIR supercontinuum source for broadband (1.55 µm - 4.5 µm) sample illumination. Hyperspectral imaging capability is achieved by a single micro-opto-electro-mechanical digital micromirror device (DMD), which provides both spatial and spectral differentiation. For that purpose the operational spectral bandwidth of the DMD was significantly extended into the MIR spectral region. In the presented design, the DMD fulfills two essential tasks. On the one hand, as standard for the SPI approach, the DMD sequentially masks captured scenes enabling diffraction-limited imaging in the tens of millisecond time-regime. On the other hand, the diffraction at the micromirrors leads to dispersion of the projected field and thus allows for wavelength selection without the application of additional dispersive optical elements, such as gratings or prisms. In the experimental part, first of all, the imaging and spectral capabilities of the hyperspectral microscope are characterized. The spatial and spectral resolution is assessed by means of test targets and linear variable filters, respectively. At a wavelength of 4.15 µm a spatial resolution of 4.92 µm is achieved with a native spectral resolution better than 118.1 nm. Further, a post-processing method for drastic enhancement of the spectral resolution is proposed and discussed. The performance of the MIR hyperspectral microsopce is demonstrated for label-free chemical imaging and examination of polymer compounds and red blood cells. The acquisition and reconstruction of Hadamard sampled 64×64 images is achieved in 450 ms and 162 ms, respectively. Thus, combined with an unprecedented intrinsic flexibiliy gained by a tunable field of view and adjustable spatial resolution, the demonstrated design drastically improves the sample throughput in MIR chemical and biomedical imaging.