Due to unforeseen events this weekend (my now fiance driving up from Charleston to surprise me, in costume, with a proposal at a ball) I don't have quite enough time to make a full post on my cutaway gown, but I will at least try to get a basic history section!
Here is the infamous portrait by Ducreux that shows a beautiful example of the style. While this gown was most popular in the 1780s, it did actually show up in the colonies in the late 1770s and continued to be worn throughout the '90s as well.
Obviously, most of the gowns seen in portraits are made from silk taffeta, but a cotton print would be lovely as well. For some reason, I seem adverse to linen, but I can't give a particular reason why. Both solid colors and smaller stripes are acceptable. The large 2 or 3" stripes seen earlier in the century would have been out of style by this point. You can also choose a contrasting fabric for the leftover zone in front and even the petticoat.
In terms of the actual cut, there are a number of different looks to the front and to the sleeves. At this point the back would have usually been quartered rather than an English style. You could cut the CB pieces flat on bottom and connect them to the skirt to give that illusion of continuance without actually pleating the bodice if wanted.
Above you can see three examples of both front cut and sleeves. Simplifying it, you can choose a straight angle or to curve it away. From there, whether it will be a split zone piece or not. And if it will be whether you fasten by pins, hooks, or buttons. You can also add a tab, as I did, across the top of the front. The sleeves can be the regular elbow length style, full length (you may choose to have the wrist area button since they're tightly fitted), or even cap sleeves over a contrasting long sleeve. It gets more complicated when building, but that will come later.
The back, as talked about, is shown with two different styles of quartered backs.
Of course, in this period especially, accessorizing can make all of the difference. Be it through a sash or ribbon around the waist, a crossed over kerchief, lace, or the ever popular hedgehog hair with ribbons, feathers, or over-the-top hat. It's easy to see, from some of the portraits below how this style of gown evolved into the separate over-gown near the end of the century.