When creating a new garden, and sod or weeds are in the way, I don't use chemicals or a sod cutter, I use the "No Dig" method to create a beautiful garden with less work.
Create the line of the new garden by cutting into the existing sod or grass, then go ahead and place and plant your shrubs, trees and perennials. That's right, plant them right into the grass. Next, follow with layers of newspaper, twelve (12) sheets thick. Cover everything with the newspaper, right up to the roots of your new plants. Be sure to use only newsprint (none of the glossy inserts) and overlap the layers (you don't want any pesky weeds and grasses finding a way through). As you are layering the newspaper, cover with compost to help with the decomposition of the unwanted plant material and to feed the soil for the new plants.
The final step is to cover the new garden with a minimum of three inches (3") of mulch. This will aid in the smothering of unwanted plants and give you a beautiful finished look to your garden (see my previous post for the other benefits of mulch!) and all the hard work will happen under the mulch and paper, while you enjoy your new garden!