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To pulverize something. A noun or pronoun can be used between "grind" and "up." My daughter has a hard time swallowing pills, so I grind up her antihistamine tablets and put them in her yogurt. Good news—the landscaper was able to grind all those tree branches up.
grind something up
to pulverize or crush something by crushing, rubbing, or abrasion. Please grind the fennel seeds up. Grind up the fennel seeds and sprinkle them on the top.