Grant did have a peculiar mindset when it came to the dead and wounded at Vicksburg - I think the Confederates were right and it worked. Pemberton did surrender shortly after, and he was the one who had to ask Grant to retrieve the wounded. Grant did the same at Cold Harbor and he and Lee went back and forth about it. It sounds petty and prideful but actually it was calculated. Grant wanted Lee to ask for a cease fire to get the men, and that was just about the same as admitting he was the one defeated. Lee was not defeated. It was important that Grant be the one to ask - he was the one who lost.
When you have two really good, really determined, really formidable generals fighting like Lee and Grant, there are going to be massive casualties. It seemed to people in the North that Grant was uncaring for the lives of his men. It wasn't that - it was that the AoP was an army and he used that weapon liberally, more so than any of his predecessors. Lee, for his part, had no choice. His army was never meant to sit and do no fighting - he had forged a fine weapon and he used it.