Dinoflagellates are marine organisms that undergo seasonal proliferation events known as algal blooms. Vegetative cell proliferation is a main contributing factor in these events. However, mechanistical understanding of mitosis and cytokinesis in dinoflagellates remains rudimentary. Using an optimized immunofluorescence protocol, we analysed changes in microtubule organization occurring during the mitotic cycle of the toxic dinoflagellate Ostreopsis cf. ovata. We find that the flagella and the cortical microtubule array persist throughout the mitotic cycle. Two cytoplasmic microtubule bundles originate from the ventral area, where the basal bodies are located - a cortical bundle and a cytoplasmic bundle. The latter associates with the nucleus in the cell centre before mitosis and with the acentrosomal extranuclear spindle during mitosis. Analysis of tubulin post-translational modifications identifies two populations of spindle microtubules - polar acetylated microtubules, whose length is constant, and central tyrosinated microtubules, which elongate during chromosome segregation. During cell division a microtubule-rich structure forms along the dorsal-ventral axis, associated with the site of cytokinesis, consistent with a cytokinetic mechanism that is independent of the actomyosin ring typical of animal and yeast cells.