There’s an older card similar to this called Overrule, which is from Dissension. It was XWB, with the same permission effect, except that you gained X life instead of dealing damage. Again, you gained that life whether or not the spell became countered. A counter-spell that can also deal damage whether or not that spell gets countered is a very good card. You don’t usually see permission spells that get more powerful as the game goes along. So was this card a key to making counter-burn a real deck in Standard again?
Unfortunately, as good as Mindswipe is on paper, it never really saw much competitive Standard play. It did work its way into a Top 8 Jeskai Control deck as a four-of. Also, some Jeskai Tempo decks like this one would run a single Mindswipe. But beyond that, it didn't see much top level play. It's never really made its way into Modern, either.
Unsurprisingly, though, Mindswipe does see a fair amount of play in Commander. It's also unsurprising that the Commander who takes the best advantage of this card is Mizzix of the Izmagnus. This is because Mizzix makes X spells very good, since her experience counter ability makes instants and sorcery spells cost 1 less for each experience counter that you have. It's a very powerful card in that deck.
Also, Mindswipe sees some play in Melek, Izzet Paragon spellslinger decks, in which Melek can actually copy Mindswipe and deal double the damage as well as giving you a second chance to counter that spell in case the cost was paid initially. While these aren't the only two commanders that have used Mindswipe, these are the two that will take advantage of this counterspell the most.
Mindswipe is a solid card. But you have to really dump a lot of mana into it in order to get the full value from it. While it seemed like it would be a decent card in Standard, it wasn't played much. While the damage is a nice bonus, most of the time you may only get in 1, 2, or 3 damage. That's nice, but it didn't really find a home in most decks that would want it. But in Commander, having this as part of your counter-magic suite, where mana is much more plentiful, can allow you to both stop a crucial spell and deal a fair amount of damage. While Mindswipe isn't worth much, it's worth having around for Commander players.