It's been too long for me to say for sure, but... maybe? It's certainly more open than probably most of its contemporaries, but probably only deceptively so, like there were only so many ways to approach things and most stuff is still locked in sequence as it would be in any linear RPG. A little more Zelda than Final Fantasy, but there's still a critical path.
Some of the other Mana games blow that wide open though. The next game in the series had a choice of like six playable characters each with their own origin points and intertwined stories - pretty crazy for the SNES days. That's the one I really want to see rereleased or remade or just given a proper English translation that isn't a ROM hack.
But if there's a "right" way to play Secret of Mana, it's with a second player, or with three players on a multi-tap, since it's one of the rare RPG-like things in that era with multiplayer support. My sister and a friend and I ran through the whole thing that way when we were kids and it was fantastic.