Skilled Dark Magician's effect in response to attack
No you can't, because Skilled Dark Magician's effect is Spell Speed 1. In other words it is not a quick effect. This we can see from it's text:


  Each time a Spell Card is activated, place 1 Spell Counter on this card when that Spell resolves (max. 3). You can Tribute this card with 3 Spell Counters on it; Special Summon 1 "Dark Magician" from your hand, Deck, or GY.


We can see that it does not include "during either player's turn," or "(Quick Effect):", in it, which are the ways to know if some effect can be activated as a Quick Effect (Spell Speed 2+). For example, check the text of Crystal Wing Synchro Dragon to see an example of such wording.

This means that you can only activate it's effect during your turn (and only during your Main Phases), thus you can't do it during your opponent's Battle Phase.



If I may suggest, a card that could be really useful for you is Magical Dimension, which happens to be quick-play so you could indeed use it to "block" the attack by forcing a replay when the attack target leaves the field (and even destroy a card while at it):


  If you control a Spellcaster-Type monster: Target 1 monster you control; Tribute that target, then Special Summon 1 Spellcaster-Type monster from your hand, then you can destroy 1 monster on the field.