1. The Gemara understands that there is no obligation to have Simchah with the meat of a Korban on the first night of Yom Tov.
2. Rav Papa: There is an obligation of Simchah on the first night of Yom Tov.
3. Rabin: One may fulfill his obligation of Simchah on the first night of Yom Tov by eating the meat of a Korban.
4. The Gemara offers a different explanation for why there is no obligation of Simchah on the first night of Yom Tov.
5. The Mishnah discusses how a person may be liable for transgressing Shabbos while offering a Korban Pesach on Erev Pesach.
A BIT MORE
1. Since the verse excludes part of Yom Tov from Simchah by saying, "Ach Same'ach" ("Ach" being an excluding word), we presume that it refers to the first night of Yom Tov. This is because no Korban is brought on Yom Tov that would cause such Simchah.
2. Even though this Simchah cannot be achieved through Korbanos (see #1), it is achieved through wearing nice and clean clothes and drinking good wine.
3. Even though the Korban was slaughtered before Yom Tov, there is no requirement that the Korban be slaughtered on Yom Tov in order to fulfill the Mitzvah of Simchas Yom Tov with it.
4. The Gemara understands that the first night is excluded from "Ach Same'ach" (see #1 above) and not the last night. This is because there is an obligation of Simchah during the time before the last night of Yom Tov, whereas there is no such obligation during the time before the first night of Yom Tov.
5. For example, if he accidentally slaughters it intending it to be a different Korban, he transgresses Shabbos.