Q.How do I kill thistle?
I cut the weed as close to the ground….I “dribble” a weed killer on the open cut stem…and yet it comes back.

Cut stem treatment is not as effective for thistle as spraying or painting the leafy tops for foliar absorption with a systemic herbicide.
You don't identify the type of thistle, describe the site, - pasture, lawn or planting beds or un-planted soil surface, and you don't state what herbicide you have been using.
To spray in a lawn area use an herbicide for broadleaf weed control like this: https://www.domyown.com/msds/SpeedZoneLawnWeedKillerConcentrate-SL_label.pdf
But the active ingredients will kill other broadleaf plants, so don't use near desirable plantings.
https://www.gardeningknowhow.com/plant-problems/weeds/canada-thistle-control.htm