As soon as I am makdish (sanctify) an animal for a korban it is now owned by the beis hamikdash. To the extent that if I were to use that animal to do work for me I would be chayav for meilah (stealing from the temple). If so, how can a person ever bring a korban? The korban has to be yours yet as soon as you are makdish it it is no longer yours!?
it is built in to the system that this is how you bring a korban and it is considered yours even though as you pointed out it is not technically yours.
ultimately, nothing is really yours as written: "The land shall not be sold permanently: for the land is Mine; for you are strangers and sojourners with Me" (Vayikra 25:23), does not mean you're exempt from maaser or other mitzvos which require that the land be yours. so it's built in to the mitzva that in such a case, it's considered yours even though technically it's not
האומר חטאתו ועולתו ואשמו ושלמיו של פלוני עלי, אם רצה אותו פלוני הרי זה מניחו להקריבן על ידו ומתכפר לו, רצה בשעת הפרשה ולא רצה בשעת הקרבה אלא חזר בו בעולה ובשלמים מקריבין ומתכפר לו בהן, אע"פ שאינו רוצה עתה שהרי רצה בשעת הפרשה, אבל בחטאת ובאשם לא נתכפר לו עד שירצה מתחלה ועד סוף.
[The following laws apply when] one says: "I promise to bring the sin-offering, burnt-offering, guilt-offering, and peace-offering of so-and-so." If that person agrees, he may allow him to bring those sacrifices for him and he receives atonement thereby. If he agreed at the time [the sacrificial animals] were set aside, but reneged and did not agree at the time they were offered, with regard to a burnt-offering and a peace-offering, they should be sacrificed and he receives atonement through them even if he does not consent at this time, because he agreed at the time [the sacrificial animals] were set aside. With regard to a sin-offering and a guilt-offering, by contrast, he does not receive atonement unless he consented from the beginning until the end. (translation from chabad.org)
There are two types of me'ilah -- abusing an intrinsically-sacred object (e.g. this cow belongs to me! But it has been consecrated to be brought as a sacrifice and therefore can't be used for anything else), and misappropriation of Temple property (e.g. this is a plain old hammer. It's supposed to be used for hammering. But it was Temple property, so I can't use it for hammering my own carpentry project.) The quantity threshold for punishment differs between them: for the former, it's the quantity of sacred material abused (e.g. a non-Cohen burned a kezayis of terumah), the latter by monetary value (we can't punish for monetary matters less than a shaveh prutah.)