Some dead plant stems and leaves can be easily cut down and turned into mulch. Remember that birds and insects rely on standing flower stems and seed heads to survive over winter, so leave as many of those as you can. However, healthy stems of tomatoes, peppers, asparagus, etc would be of better use laying on the ground as mulch. You only need to remove plants if they were infected with disease or destructive insects. Focus on attracting beneficial microbes and insects and nature will balance things out.
Cut the plants off at the base of the stem. There is no need to dig up plant roots, that only disturbs and hurts the soil microbiome. Cut up stems so they can lay flat on the ground. If the central stem is more than a half inch in diameter you may want to put it in a long-term compost pile to break down so it doesn’t get in the way of planting in the spring.
Links to More Information
Delay Garden Cleanup to Benefit Overwintering Insects https://extension.psu.edu/delay-garden-cleanup-to-benefit-overwintering-insects
Chop and Drop https://www.growingwithnature.org/chop-and-drop/
