לֹא-תִקֹּם וְלֹא-תִטֹּר אֶת-בְּנֵי עַמֶּךָ, וְאָהַבְתָּ לְרֵעֲךָ כָּמוֹךָ
Do not take revenge, do not hold a grudge; you shall love your fellow [Jew] as yourself. Vayikra 19:18
I don't need to be commanded to love my friends. Chazal, in fact, say that this mitzvah applies to condemned murders (K'subos 37b, Sanhedrin 45a; thank you Torah T'mima). Remember that to have a condemned murderer means that two kosher witnesses warned him, and he said "I know, but I am doing it anyway", and then proceeded to murder another Jew in cold blood before those two witnesses. And the Torah says about that murder, "love your fellow [Jew] as yourself". Moreover, R' Akiva says, "this is a great rule/fundamental principle of the Torah" (Yerushalmi Nedarim 9:4).
Klal Yisrael is one entity. If an organ or limb becomes diseased, we do whatever we can to save it. When I worked in radiation therapy unit, we once had a young man (20s) with cancer in his leg. It would have been very simple to ensure his cancer didn't spread: just remove the leg above the tumor and be done with it. Of course he didn't want that and we were doing what we could to save his leg. He would suffer the rest of his life with the side effects: swollen, stiff, and painful hip and knee joints; but that was worth it to save his leg. On the other hand, if a limb could not be saved (gangrene, for example), they you remove it; one limb is not worth a life. Even when the limb is removed there is no joy, certainly no feelings of revenge or holding a grudge against the diseased limb. In fact, a person in that situation mourns the loss, examines his behaviour to see if it could have been prevented, and does everything to prevent that from happening again.
Zeh klal gadol ba'Torah.