Keeping thistle plants stressed is one key component to exhausting its stored resources, so cutting it back and/or mowing is one way, and definitely do not let it flower and go to seed (if it does flower/seed, remove it by hand as mowing will simply spread the seed around). 

There are herbicides available that you could use a small paint brush to paint onto the thistle. When doing so with a paintbrush you're sending the herbicide into the vascular system of the plant while simultaneously preventing damage to the surrounding plants. Canada thistle tends to spread by both seed and rhizome (the root system is also your enemy). Please see these brief fact sheets on recommended herbicides and other control tips:
https://adams.extension.colostate.edu/ag-acreage/canada-thistle/
https://drive.google.com/file/d/1VD0akK6512uYeraw77xI7XVKujmUh81u/view

Before we recommend the best control for the cornflower, we want to make sure that we are recommending controls for the right plant. Please see these links below and let us know if one of these plants are the ones you are trying to eliminate from your yard. Better yet, do you happen to have pictures that you could email to me of the plants from your yard?

Annual Cornflower: https://www.missouribotanicalgarden.org/plantfinder/PlantFinderDetails.aspx?taxonid=277177
Perennial Cornflower: https://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=h570

Please feel free to contact me directly if you have any questions. I can be reached at <personal data hidden> and/or
<personal data hidden>.

Merrill Kingsbury 
Master Gardener Program Coordinator 
CSU Denver Extension