Does the draw from a cantrip spell go on the stack separately from the spell itself?

When a cantrip spell (e.g., Opt or Gitaxian Probe) resolves, all of its effects — including the card draw — happen during that single resolution. The draw is an instruction on the spell itself, not a new object placed on the stack. Per CR 608.2, a spell resolves by following its instructions in order, so the draw simply happens as one of those steps.

This means opponents cannot respond "between" the spell and the draw, because there is no window there. After the spell fully resolves (including drawing), both players receive priority again (CR 116.3), at which point they may respond to whatever was drawn or played next.

The only way a draw effect goes on the stack as a separate object is if it is a triggered or activated ability (e.g., a "whenever you cast a spell, draw a card" trigger). Those triggers are placed on the stack after the spell resolves and can be responded to independently (CR 603.2).

Concrete example: You cast Opt. Your opponent lets it resolve. During resolution you scry 1, then draw 1 — both happen as part of Opt's single resolution. Your opponent cannot cast Trickbind or otherwise interact between the scry and the draw; Opt is already off the stack.