There's a few options I can see to execute this design cleanly.

1. Use a laser cutter to cut the velvet. This will slightly melt the edges of the fabric, preventing it from fraying. Full synthetic velvet will be fully sealed, and velvet from natural fibers will have minimal fraying. (source)

2. Use a product like Fray-Check on the back of the fabric to seal the edges, before or after cutting. Anti-fraying products tend to have a thin superglue-like consistency and you'll want to test them before using them to make sure they don't bleed through to the pile and damage the appearance of the velvet. Application will likely be easiest prior to cutting.

3. Use a "reverse applique" technique. In this technique, you'll sew a panel of velvet behind the red fabric, then stitch in the edges of the design you wish to create. After cutting away the fabric in front, the velvet will be revealed, and you can then finish off the edges of the red top layer. You'll be left with a very similar look without the issue of shedding or fraying from the velvet being cut, including leaving the pattern in the red fabric aligned between pieces. You can find numerous tutorials on the process online; here's a basic guide.

There's a few options I can see to execute this design cleanly.

1. Use a laser cutter to cut the velvet. This will slightly melt the edges of the fabric, preventing it from fraying. Full synthetic velvet will be fully sealed, and velvet from natural fibers will have minimal fraying. (source)

2. Use a product like Fray-Check on the back of the fabric to seal the edges, before or after cutting. Anti-fraying products tend to have a thin superglue-like consistency and you'll want to test them before using them to make sure they don't bleed through to the pile and damage the appearance of the velvet. Application will likely be easiest prior to cutting.

3. Use a "reverse applique" technique. In this technique, you'll sew a panel of velvet behind the red fabric, then stitch in the edges of the design you wish to create. After cutting away the fabric in front, the velvet will be revealed, and you can then finish off the edges of the red top layer. You'll be left with a very similar look without the issue of shedding or fraying from the velvet being cut, including leaving the pattern in the red fabric aligned between pieces. You can find numerous tutorials on the process online; here's a basic guide.

The more I look at the original image, the more I feel it's likely that the original process used was Reverse Applique. It's a very old technique highly compatible with hand-sewing, which likely was how a dress like that would have been produced historically. It's likely also the most time-consuming process, so if the goal is replication of the appearance over historical accuracy, the other options will provide a similar look more quickly.