Pyrrhic no, attrition yes by circumstance and necessity. In Grant I don't see a ruthless man, but I do see a pragmatic duty-bound one. I don't get the impression he was forced to dehumanize his own soldiers or those of the enemy to succeed. Succeeding in a war is really a mathematical/tactical equation. But by pragmatically pressing his advantage it can also be argued that Grant instead: Saved more lives due to the majority of casualties being the result of disease as the war dragged on. Saved the country from ongoing costly sectional warfare for decades. Really the only claims that can be made against Grant, his motives or his tactics is if one wants to try to prove that he was one of the following:
Willfully careless
Tactically negligent
Motivated by revenge, hatred, retribution, blood lust or some other non-military factor
Grant did not relish the prospect of a protracted war of attrition, but if necessary to fulfill his duty he was willing to engage in one. Although one can certainly argue all battles/wars have inevitable elements of attrition both in lives and supplies. Grant had a desire to reduce casualties for both sides if possible but his view of prospective casualties was much broader than simply the battle/campaign he was currently engaged in. All the previous commanders had failed, flinched and withdrawn prolonging the conflict and leading to the inevitable higher overall casualty rate due to disease. If one does the math it would seem to vindicate this broader and longer-term view of casualties that Grant operated from.
Grant clearly wanted to find any path forward to end the war that would ultimately preserve the Union. If in fulfilling his assigned duty (assigned by superiors) he had to make difficult decisions that would lead to the loss of life, he was willing to do it, but always regretted the corresponding loss in casualties. Someone who is not willing to order men to their deaths to fulfill his duty is obviously not going to be an effective commander during Grant's time. He knew from Shiloh that he could and would be scrutinized and demonized for casualties but he remained focused on his powerful commitment to the cause. Grant saw no glory in war, but He had a pragmatic outlook that allowed him to grasp the bigger picture. The needs of the many outweigh the needs of the few. He didn't start the war, but it was his duty to end it as quickly as possible for the perceived benefit of the entire population of the nation and future generations both on and off the battlefield and around the world. It was mathematical. Ending the war quicker militarily, given the prevailing circumstances required high casualty rates. The stakes were high, that's what drove men to the level of conviction where they would voluntarily sacrifice their life for the cause. After the war Grant took personal responsibility for casualties and I can imagine the heavy burden of responsibility and horrors of the battlefield haunted him to his death.