How can we slow down mitosis and meiosis or one of the two especially mitosis and what can be brought about?

If you are talking about mitosis and meiosis specifically, then vinca alkaloids and taxanes can inhibit microtubule assembly and disassembly, respectively. Eg. Vincristine, vinblastine, paclitaxel, docitaxel. They are used for chemotherapy. The antifungal equivalent of microtubule inhibitor is griseofulvin.

 

If you are talking about slowing down the cell cycle, then most cell-cycle specific chemotherapeutic agents can disrupt cell cycle turnover at various stages.