Yes, you can use a hoe to get rid of grass by using the flatten or pathen options. Right-click while holding the hoe to choose what you want it to do. Flatten tries to raise/lower the ground at the level you're standing on. It can only change the height so much before it may need additional help, like using the raise ground option, or a pickaxe to lower it more.

Later on, once you get a cultivator, you can use that to restore any grass that you have altered if you want.