Does a counterspell that says 'counter target spell' work on a spell that has already begun resolving?

A spell exists as a legal target for counterspells only while it is on the stack and has not yet begun to resolve. Once the game moves to resolving a spell, that spell is no longer a spell 'on the stack' in a targetable sense — it is mid-resolution and the game is executing its instructions.

Per CR 608.2, when a spell begins resolving, it is removed from the stack as part of that process (for instants and sorceries, it moves to the graveyard after resolution). Counterspells require a target to be declared when the counterspell is cast (CR 601.2c), and the target must remain legal upon resolution (CR 608.2b). A resolving spell is no longer a legal target.

Additionally, CR 116.3 clarifies that players only receive priority between spells and abilities resolving, not during resolution. This means there is no game window in which you could even cast a counterspell while another spell is mid-resolution.

Concrete example: Your opponent casts Fireball and it begins resolving. You cannot cast Cancel at this point — there is no priority window, and Fireball is no longer a valid target on the stack. You would have needed to cast Cancel before your opponent's spell began resolving, when both players passed priority.

In short, 'counter target spell' can only interact with spells sitting on the stack awaiting resolution, never with one that is currently resolving.