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Spiderwort plants need to be kept moist, so there's a possibility that your plant simply needs more water than it's currently getting, particularly in the zone you're in (where the temps have been unseasonably hot early in the summer). Mine do the same thing when they're thirsty (and they stop blooming, of course).

This article will give you some additional information on caring for your spiderwort plant:

https://www.gardeningknowhow.com/ornamental/flowers/spiderwort/growing-spiderworts.htm

Yes, you can cut back after flowering. They will likely bloom one more time for you.

https://www.gardeningknowhow.com/ornamental/flowers/spiderwort/growing-spiderworts.htm

I would suggest trimming spiderwort's early growth back by one-half, deadheading after the first bloom by cutting back one-half again, and reducing the plant's height by two-thirds after blooming has stopped.
https://www.gardeningknowhow.com/ornamental/flowers/spiderwort/growing-spiderworts.htm

Yes, spiderwort may die back in summer heat especially if it gets afternoon sun. If the stem is green, cut back spent blooms to the next long leaf. This is where new blooms may occur. If they have gone soft and yellow, cut down to the ground. They will come back.

Native or garden spiderworts have three blue or purple petals to tropical spiderworts' two and bloom for several weeks atop clumps of smooth, lance-shaped leaves 18 to 24 inches tall. Snap off flowers as they fade to prevent self-seeding, though these plants are not considered invasive.
https://www.gardeningknowhow.com/ornamental/flowers/spiderwort/growing-spiderworts.htm

This is a common problem with spiderwort. The usual suggestions are to grow it in partial shade and to cut it back to 12 inches after the initial bloom period to stimulate a second bloom. They are placed 4-6 inches deep when planted. Fertilizer encourages excessive (read floppy) growth in most native plants, spiderwort included. At the Lady Bird Johnson Wildflower Center, spiderworts are placed next to taller plants or rocks to lean against. I wonder if dividing the clump will help the plants stay upright. Give it a try this fall or early next spring. Of course, a plant hoop or sticks and twine can be employed to keep your spiderwort upright.