Blot the stain with a clean, white cloth. Keep blotting until no more of the stain is transferred to the cloth. Do not rub the stain; this only works it deeper into the suede's fibers.
Spray or blot a suede cleaner onto the suede's fabric. Follow the label's instructions for application method and amount. Keep applying and blotting until no more hair dye is transferred to the cloth.
Steam-clean the stain. Run the nozzle of the fabric steam cleaner over the stain for 10 seconds at a time. Then blot the stain with a clean cloth. Keep steaming and blotting until no more stain is transferred to the cloth.
Call a professional leather and suede cleaner, if other methods aren't working. More vigorous cleaning must be done with specialized dry-cleaning chemicals only available to expert suede cleaners.