Use caution mowing Poison Ivy, as you don't want to aerosolize its irritating sap where it could be inhaled or land on skin. Sap will also contaminate the mower blades (which should be sharpened every spring and fall season, ideally), and unless washed off with detergent, might remain on the equipment (and able to irritate skin) for over a year.

Spot-treatment with herbicide can work, but the chemical used needs to be systemic (absorbed by foliage and moved into roots), might need more than one application (follow product label directions regarding any interval to repeat), might benefit from a surfactant, and would require that the treated plant(s) not be mowed for some time after application so the chemical has time to be absorbed and moved into roots. A surfactant is an additive to certain pesticides that helps them function well, and in this case, would be a "spreader-sticker" that helps the spray adhere to the ivy's water-repellent foliage. They are sold alongside pesticides in garden centers, but make sure the herbicide chosen allows for its use (some formulations might not need one), and follow the directions on both bottles. The more of the plant you can treat with systemic herbicide, the better it will work, so if you can't spray all of its foliage, you might get only partial control from a treatment. If you were using a non-systemic chemical, then spot-spraying won't accomplish much unless you can keep up with treating all foliage as promptly as it re-appears after each die-back. Eventually, that tactic will exhaust roots of stored energy for regrowth, but that might take months or even years for a well-established, older plant.

Miri