Do I cut it down after it is dead.
Yes. It will need to be replanted next season. This article will help:
https://www.gardeningknowhow.com/ornamental/vines/hyacinth-bean/purple-hyacinth-bean-care.htm
will the hyacinth bean vine grow successfully in the upper peninsula of MI?
hey take three months to mature, so you may not have any flowers till late summer. Get the seeds in the ground as soon as you have your last frost or buy transplants if they are available. Be sure to harvest any seed pods before the first freeze.
https://www.gardeningknowhow.com/ornamental/vines/hyacinth-bean/purple-hyacinth-bean-care.htm
Rec'd seeds as gift - no instructions on planting - depth & spacing
You can direct sow outside with about six seeds per foot, planting about 1/2 inch deep in the soil. When true leaves appear, thin to 12 inches apart. Be sure you have a sturdy trellis. Here is more:
https://www.gardeningknowhow.com/ornamental/vines/hyacinth-bean/purple-hyacinth-bean-care.htm