Even though washing one's body is forbidden on Yom Kippur, nevertheless, Netilath Yadayim (the ritual washing of one's hands), in the morning after waking, is required. The difference is that one may only wash one's hands up to the knuckles closest to the wrist and not up to the wrist, as is done on other days. It is appropriate to have in mind that the washing is for the purpose of removing the evil spirit that rests on them at night, and not for pleasure. The same applies to Netilath Yadayim after the bathroom.
If there is dirt on one's body, including in one's eyes when one wakes up, one may wash the dirty area only. Care must be taken not to allow the washing to extend beyond the area which is dirty. Again, it is appropriate to have in mind that the washing is for the purpose of cleanliness and not for pleasure.
Washing or rinsing one's mouth in the morning to get rid of the bad taste or smell, is forbidden. One is not permitted to swish water or mouthwash in one's mouth, or chew spices or gum, even if one spits it out immediately, and even if one's head was facing down all the time so as not to swallow any of it.
(See Ner LeSion, Yom HaKippurim, 11:14-16)
Yom Kippur, Yom Hakippurim, washing mouth on Yom Kippur,