For Redwood trees this is normal and healthy, they could be called
"suckers" but actually add energy to the root of the tree and are the
back up sprouts if anything goes wrong with the main tree. They can
even develop into large trees of their own. If it important to remove
them for ascetic reasons then just prune them back to the trunk and rub
out sprouts as they appear, otherwise just let them grow.

Richard Reames
http://www.arborsmith.com