The best way to clean a mohair garment is to use a light detergent meant for wool. Wash the product gently by hand in warm water. Do not agitate the mohair too much, as it can felt in the process.
Mohair should not be washed often. As a type of wool, hot water and agitation can felt it. Felting is a process that some crafters encourage intentionally to create a strong, dense fabric. However, if you like the size and shape of your mohair garment or object, you do not want to felt it further. Felting causes the garment to shrink; it also melds the fibers together, almost like matting.
Therefore, in between washings, shake out the mohair to release any dirt or debris. After washing it gently, you can use the washer to release the excess water in a spin cycle. Once you have removed the excess water, lay it flat to dry or hang it up.
On the other hand, if you want to clean raw mohair fiber (a fleece), you need to use very hot water. Mohair contains "yolk," the natural grease from the animals. Try placing the fleece in a loose netted bag, and thoroughly dunking it into hot water mixed with detergent. Soak the fleece for at least half an hour before checking it to see if it has released the grease. If it hasn't, turn the fleece over to soak some more. However, make sure not to agitate the fleece too much, as that can lead to felting.