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You can cut back after blooming. After a dormancy, it should grow and bloom again.

https://www.gardeningknowhow.com/ornamental/flowers/portulaca/portulaca-plants.htm

This is a personal preference. I trim them when they start getting ratty-looking and to collect seed. Often you can tell where a new branch is emerging from an old stem. Don't cut this off. You can go for a quicker and more drastic cut if there is time for the plant to recover and rebloom before frost. Moss rose loves hot weather and direct sun. If you are in the northern hemisphere, the weakening sun and decreasing hours of daylight mean less vigorous growth in sun lovers. Where I live, frost is due in 3 weeks!

These are pretty drought tolerant, and don't like to remain wet for long. I would also add dolomitic lime around the area, as it looks like your pH may be a bit off in your soil. Here is an article on their care: https://www.gardeningknowhow.com/ornamental/flowers/portulaca/portulaca-plants.htm

My guess is that a mammal has caused this damage, since rabbits and probably other mammals will eat this plant. Snails and slugs could also be the culprit, but if the slug pellets haven't worked, maybe that is less likely. Do check the area for slugs and snails and remove them by hand if you see them. Here is some advice for dealing with rabbits in the garden. There are also articles on mice, voles, and other mammalian pests on the website.

https://www.gardeningknowhow.com/plant-problems/pests/animals/keep-rabbits-out-of-gardens.htm

Portulaca is an annual which means it flowers, produces seed and dies in one season. It is easy to collect portulaca seed and there is a good chance that you will have seed sprouting under your hanging basket's location. If you have a hybrid variety, you will lose some of the vibrant color you had this year. I grew portulaca for several years by collecting seed. Each year I had more yellow flowers than the year before. It could be that yellow seeds are more vigorous or that the hybrid was reverting back to the original plant. If you have seed to collect, keep it in a dry, cool place. You can simply scatter the seed next spring where you want it to grow. Most tiny seeds need light to germinate so don't cover them, just lightly press so there is good contact between seed and soil.

No plant is safe from hungry deer but portulaca is listed as deer resistant.