There aren't too many places you can use Cut at this point, but you'll occasionally see those small trees blocking your path. They usually lead to helpful items or shortcuts. In fact, if you head back to the Virbank Complex, right before you enter the main part of it, there's actually a path heading west that you can follow to find a small tree to whack down — behind it is a Super Potion.Down by the harbor, you'll find there's some Team Plasma Grunts, as well as Roxie and Hugh. Go ahead and fight the Team Plasma Grunt right in front of you, who uses a Patrat L14. After beating him, he and his goons run off. Roxie is about to chase them, but lets them go, stopping instead to give you HM01 (Cut) instead, which can be used outside of battle to cut down small trees. Keep in mind that HM moves cannot be forgotten, except by the Move Deleter, and since Cut is a pretty lousy attack, I recommend putting it on something that you don't plan on using in battle. Patrat is a Pokemon that can learn Cut and is pretty easy to get.
Anyway, you're going to need to chase down those Team Plasma Grunts right away! Head back on over to Route 20 to the west whenever you're ready.