You could certainly Dash first to increase you movement allowance, then attack the first mook, then move, then attack the second mook. That's not exactly what you're asking about though, since you want to see the result of the first attack before deciding to Dash.

In the strict rules as written, however, only movement is explicitly allowed to be broken up arbitrarily. Taking the Attack action doesn't "add to your attack allowance" the way Dash adds to your movement allowance.

Implicitly, when you take an action, you are committed to completing the entire action unless you have a rule that says otherwise. "Moving Between Attacks" is one such rule, and object interaction (PH p.190) is another:

You can also interact with one object or feature of the environment for free, during either your move or your action.

By this reading, you have to complete all the Extra Attacks that are part of the initial Attack action before using Action Surge to Dash.

The quoted section refers to the fact that one grapple attempt uses up only one attack and not a whole Attack Action.

Thus multiple attempts to grapple can be made in a turn if you have Extra Attacks.

This is also supported by Jeremy Crawford, who says:

If you take the Attack action and have multiple attacks, you can replace any of them with a grapple/shove.

(Thanks to Doval, who found this tweet.)