A weed on the dirt would likely grow in the new spot, and gripping is tricky. But to your point, what about just a spike or hammer or blade to just mash the weed? More simple than a grip.
Plants can be weirdly resilient to smashing -- various bits of plant fragments can decide to grow new roots.
Chuck the weed in a barrel and take it away somewhere to be killed. Apparently a compost pile will kill weeds (and their seeds) if at a hot enough temperature long enough.
You could also heat it in place. Propane is not really a pesticide, but it works nicely. An electric arc should also work nicely, even burning out the root.