If Vault 87 leaves the battlefield before its first chapter ability resolves, you won't gain control of the target creature at all.
2024-03-08 • wotc
The target of Vault 87's first chapter ability only needs to be a non-Mutant when that ability is put onto the stack and when that ability resolves. The control effect won't end if it later becomes a Mutant (perhaps because of the effect of the second chapter ability).
2024-03-08 • wotc
Use the greatest power among Mutants you control as Vault 87's last ability resolves to determine how many cards to draw.