A plant being labeled a perennial is only a description of its lifespan - a perennial is a plant that lives more than two years (technically trees are considered perennials, although seldom described in that way). Not all perennials should or can be divided.

Growth habit is the best way to determine if a plant can be successfully divided. If your clematis has multiple stems arising from the root crown, then you should be able to divide it. There is always a risk you will damage the root mass during this process and put both the mother plant and any offspring at risk. Personally, I'd consider layering to increase my plants before digging up and attempting to divide a large, established clematis but that's just me :-)

Yes, collecting seeds from the seedheads is easily done and another way to propagate clematis. Growing from seed, layering and dividing are all discussed on various clematis websites, like Clematis on the Web (COTW).