Commentary for Parah 12:3

על דבר המקבל טומאה – people and vessels.

If he intended to sprinkle upon a thing that is susceptible to uncleanness and he sprinkled upon something that is not susceptible to uncleanness, if any of the water still remained on the hyssop he should not sprinkle with it again.
[If he intended to sprinkle] upon a thing that is not susceptible to uncleanness and he sprinkled on that which is susceptible to uncleanness, even though there was still some water on the hyssop, he can sprinkle with it again.
[If he intended to sprinkle] upon a man and he sprinkled upon a beast, if any of the water remained on the hyssop he should not sprinkle with it again;
But [if he intended to sprinkle] upon a beast and he sprinkled upon a man, even though there was still some water on the hyssop, he can sprinkle with it again.
The water that drips off is valid, and therefore it conveys uncleanness as the usual hatat waters.
Section one: He intended to sprinkle upon something that is susceptible to impurity, such as a person (as in section three). Unintentionally, he sprinkled upon an animal (which is not susceptible to impurity). If there is still water left on the hyssop he shouldn't sprinkle with it again. Since the water that was sprinkled upon the animal has been made invalid for sprinkling, the water that remains on the hyssop is also invalid for sprinkling.
Section two: This is the opposite case. Since he sprinkled on something that is susceptible to uncleanness (such as an animal), meaning something that does require sprinkling, the water has not been disqualified. Therefore he can use the remaining water to sprinkle and cleanse something else.
Sections three and four: These two sections explain sections one and two.
Section five: Water that simply drips off the hyssop is still valid for sprinkling. Therefore, it continues to convey uncleanness as do hatat waters in general, which defile one who carries them or touches them. This water is not treated as hatat waters that have already been sprinkled which do not defile (see below in mishnah four).

על דבר שאינו מקבל טומאה – animals and vessels of stone.

אם יש באזוב לא ישנה – if there remains in the hyssop in order to do sprinkling, he does not need to return and to ritually immerse [the hyssop in the water] a second time, but rather he sprinkles from that which remains in the hyssop on the impure thing and the sprinkling counted for him. As is it is written (Numbers 19:19): “The pure person shall sprinkle it upon the impure person,” until he intends to sprinkle on the impure person, therefore, when he intends at the time of ritual immersion of the hyssop to sprinkle on the impure person, he should not repeat [the dipping of the hyssop in the water,” but rather he should sprinkle from what remains in the hyssop. But if he dipped the hyssop in order to sprinkle upon a thing that is not susceptible to receive ritual defilement, since that the beginning of his immersion is invalid, so his sprinkling is invalid and he should not sprinkle with what remains on the hyssop until he repeats [the dipping of the hyssop in the water.

המים המנטפין (the water that drips off) – from the hyssop that he had ritually immersed it for the sake of something that does not receive ritual impurity, if he immersed those drops of hyssop and sprinkled from them, they are appropriate/suitable.

לפיכך הן מטמאין -because their precepts were not done, for the first immersion was invalid, and behold, these drops are like the rest of the waters of purification that are kosher that they defile.