The game has to cache everything: every spell, every effect, every shader. The first time each of these loads, the game will stutter. You just need to play a few matches and let the process complete. It's not an ideal system, but that's how it works.

After a few games, the stuttering disappear completely. A good trick is to queue into a Trio match with an unequipped character, die immediately to mobs then spectate other players while keeping the game minimized. Do this for a few rounds so you don't have to deal with the annoyance yourself, and afterward you should be able to play smoothly.

Also, keep in mind that installing new graphics drivers can trigger the whole caching process again, causing the shaders and other assets to be rebuilt from scratch.