How did Union generals use a new type of was to defeat the Confederacy?

assuming you mean a new type of war...? Union Generals had alot more men than the Confederacy. They figured if they fought battle after battle and both sides lost about the same amount of men they would come out on top, because when the South ran out of men the Union would still have an army. Or the South would give up before that happens. That is called Total War, and it wasn't used much before the Civil War. Infact, The Civil War had more US deaths than nearly all of our other wars combined. Also, the Union wanted to capture Vicksburg and control all of the area around the Mississippi River to cut the south in half.