It is forbidden to have an incorrect intent [when performing sacrificial service with] consecrated animals, as will be explained. Therefore if one slaughtered a sacrificial animal for a different purpose or took a handful from a meal-offering for a different purpose, whether intentionally or unintentionally, he is obligated to complete the remainder of the services for the proper purpose. Even if one slaughtered [the animal], received its blood, and brought it to the altar for an improper purpose, one is obligated to cast it on the altar for the proper purpose.
Why are the laws governing a sin-offering and the Paschal sacrifice different from those governing all other sacrifices and the laws governing a meal-offering of a sinner and that of a sotah different from those governing all other meal-offerings? Because the Torah singled them out. With regard to a sin-offering, [Leviticus 4:33] states: "And he shall slaughter it as a sin-offering," i.e., that it must be slaughtered for the sake of a sin-offering. Similarly, all of its other services [must be performed] for the proper intent, as [implied by ibid.:28]: "for his sin," i.e., that its service must be performed for the sake of [atoning for] that sin. And [ibid.:26] states: "And he will atone for him," i.e., [the service must be performed] for the sake of its owner.
And with regard to the Paschal sacrifice, [Deuteronomy 16:1] states: "And you shall offer a Paschal sacrifice to God, your Lord," implying that all of the acts must be performed for the sake of the Paschal sacrifice. [Exodus 12:27] states: "And you shall say, 'It is a Paschal sacrifice unto God,' implying that it must be slaughtered for the sake of the Paschal sacrifice. Thus if one altered the purpose for which it was sacrificed or [offered for] a different owner, it is not acceptable.
And with regard to the meal-offering of a sinner, [Leviticus 5:12] states: "It is a sin-offering." And with regard to the meal-offering of a sotah, [Numbers 5:15] states: "It is a meal-offering [resulting from] envy." [The implication is that] all of the actions associated with them must be performed for that purpose.