Hilchos Maasei Hakarbanos 8:19

If the blood of a sin offering splashed on a garment but the garment was then removed from the courtyard, it is returned to the courtyard so that it can be washed there. If the garment was rendered ritually unclean while outside the courtyard, it is torn, which renders it clean. It is then returned to the courtyard and washed there. We must leave intact a piece of the garment the size of a handkerchief because Leviticus 6:20 says “garment,” meaning that what is laundered must qualify as a garment. The rest of the garment is considered ritually unclean under rabbinic law because of the part that’s the size of a handkerchief, but since most of it is torn it’s ritually clean under Biblical law and permitted to bring into the Temple in order to wash the blood from it.

Hilchos Maasei Hakarbanos 8:20

Let’s say that the blood of a sin offering splashed on the Kohein Gadol’s robe, it was removed from the courtyard and rendered ritually unclean. Tearing it is not an option because one who does so is subject to the penalty of lashes. In such a case, one brings it into the courtyard less than three fingerbreadths at a time, washing it in the courtyard as he goes. Once the robe has been cleansed of the blood a little at a time, it is immersed in a mikvah outside the courtyard.