Answer: It is fairly typical of herbaceous perennials to die back to the ground each fall. Shrubs, on the other hand, maintain a woody framework all winter.
Joe Pye Weed (Eupatorium purpureum) is a native plant that usually grows between four and six feet tall. There are some named varieties of this plant (such as "Gateway") and some of these tend to stay a bit shorter, however. This plant dies back to the ground each fall and reemerges in mid to late spring, regrows to its full height and then flowers late in the season. A mature plant will generally be larger than a newly planted one, and a plant grown in very rich and moist soil will be larger than one grown in less favorable conditions. In nature this plant is often found in low spots so, although it will grow just fine in the garden, it does actually prefer ample moisture to grow its best.
Artemisia includes a number of different plants, but most of them have silvery leaves and prefer hot sunny locations with a soil that is well drained rather than soggy, especially in winter. They are often used in herb gardens and cut for dried flower arrangements. Some types of artemisia will send out underground roots and spread very quickly, especially in a light or slightly sandy soil. Others are far better behaved and stay in a tidy clump and a few grow as a subshrub of sorts. They do however die back in the fall and the old stems should be cut away (with the exception of the shrubbier types). They should resprout in the spring from the ground and regain their full height fairly quickly.
For more information about a variety of perennials and what to expect from them, you might want to read up on them a bit. A book I particularly like is "Perennials for Dummies" by Marcia Tatroe, ISBN 0-7645-5030-6 from Dummy Press. In it you will find lots of straightforward information about various plants, how to select them to suit your planting location and how to grow them.
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