Often, yes — that is what a deposit is. Where a studio takes one, you pay part of the price when you book and the balance at the appointment. The booking page shows the deposit amount before you confirm, and the balance is whatever is left.
Where a studio does not take deposits, the whole amount is due at the appointment and there is nothing to pay up front.
What you cannot do is set your own split. The deposit is a figure the studio chose, either as a flat amount or a percentage, and it is the same for everybody booking that service. If you need a different arrangement — a payment plan for a long colour correction, say — ask the studio directly. Plenty will say yes, and it is entirely their call to make.