Canteen gourds are popular for making gourd purses. Although I haven't tackled that project myself yet, I have cut the gourds for others to make a gourd purse.
To make the cutting line straight across I needed something to hold the gourd on its side, nice and steady.
I found a small rectangular box that was close to the size I needed and was strong enough to hold the gourd steady. If your box is a little big, add some wood blocks along the sides to make a tight fit.
Find the height you want and if you have a special tool for making your cutting lines, adjust it to the height you need. I don't have one so I find a container or can that is the height I want and hold my pencil down on it. You can tape the pencil to the top if you would like.
Slide the container around the gourd marking it with the pencil. Make a vertical pencil line through your horizontal line somewhere on the gourd so you can match it up after it's been cut. I use a mini jigsaw to cut the top off.
Here are a few tutorials to help with your gourd purse project.
If you need a canteen gourd you can find some I have available that I grew here in PA.