Hi John, thanks for using Ask Extension.

Spreading by deep creeping rhizomes, Canadian thistle, can be difficult to eradicate.  Even root fragments as small as a half inch can generate a new plant.  Elimination requires persistence.  Using more than one control method can be more effective.  One method is to repeatedly dig/cut new shoots as soon as they appear (April-May), at least every two or three weeks during the growing season.  Using a targeted systemic herbicide application is also effective. This is probably the quickest and most reliable method; however, timing is important.  This should be done in early June at the bud stage and at fall regrowth (September, October). Hit it both times, once is not enough.  Spot spraying with a shield (e.g. a Jug with bottom cut out) or using a wick or sponge application can allow you to avoid damaging your ornamentals. Shading (with heavy mulch or dense ground cover) can also help but probably not on its own.  Be thorough, pulling one plant won't work. Don't till or break up the roots.  It can take more than one year to eliminate this pesky weed. Check out the following links for more detail and information:

Control Practices for Canada Thistle, Botany & Plant Pathology, Purdue U.

Removing Canada Thistle from the Home Garden

I hope this is helpful.