Very quickly or determinedly. The phrase refers to the US Civil War, in which Union forces (led by Ulysses S. Grant) brought about the Confederacy's surrender by taking the Confederate capital of Richmond, Virginia. A: "Wow, that was quick! Did you see any animals out there?" B: "No, but I went through the yard like Grant took Richmond." I barely talked to George at all today because he came through the office like Grant took Richmond.