This Tansy Ragwort informational page from OSU Extension has a section on mowing and herbicide management practices.

For mowing to be a useful management practice, do it prior to seed maturity to decrease viable seed production. Mowing too early in the plant life cycle will allow time for the plant to bolt and flower again.

Apply herbicides in the fall after rains allow green-up of rosettes or for new seedlings to emerge or in the spring before plants bolt. Specific herbicide application timings and rates differ by the type of herbicide used and the growth stage of the target weed and forage crop. Herbicide labels may also differ by intended application site (pasture, right of way, forest, etc.). Follow grazing and haying restrictions and other instructions on the herbicide labels.

In the fall, mow off dead plant material and wait for rains to stimulate regrowth of rosettes or emergence of new seedlings. The most economical herbicide treatments would be products containing premixes of 2,4-D + dicamba. For high-density infestations of tansy, use the highest labeled rates of these types of products and review the grazing and haying restrictions on individual labels. Herbicides containing aminopyralid also work well on tansy ragwort, but will likely be more expensive. Always follow the recommendations on the labels of herbicides containing aminopyralid for managing forage, manure and compost. For specific herbicide application information use the PNW Weed Management Handbook Tansy Ragwort page https://pnwhandbooks.org/weed/problem-weeds/ragwort-tansy-senecio-jacobaea.