Parashas Vayikra · Aliyah 1 · Passuk 6
Chabad.org — English translation + Rashi
Torah Temima points to Toras Kohanim (Sifra) on the order of flaying and cutting (verified).
Sefaria — Sifra / Toras Kohanim
English: “And he shall flay” — he flays it entirely, and afterward he cuts it into pieces.
Custom (order of the verbs) — the sequence “flay… and cut” teaches that flaying of the whole precedes the cutting into limbs.
The prescribed order is: flay the entire animal first, then divide it into its pieces. Cutting is not begun while the hide is still partially on.