Is the word "savage" offensive?

When applied to animals or natural forces, it means fierce or violent. When applied to human beings, it means cruel, aggressive or vicious. So, it is very negative.

As a noun, a savage means “a member of a people regarded as primitive and uncivilized”, and is thus very offensive. It is now mainly a historical term.

Savage originally meant 'wild', as sauvage does in Old and modern French. It acquired two different transferred meanings when applied to human beings; as in 'savage fighters' it became 'fierce and bloodthirsty'; though this isn't always negative (whether applied to soldiers or guard-dogs) very few people would apply it to themselves, and, however apt a nineteenth-century historian might have thought your example, it can't be applied to a whole race these days. The other meaning, of 'untamed', meant 'uncivilized' in the technical sense. (Early anthropologists used savages for peoples who had not discovered agriculture, and barbarians for those who had agriculture but not metalworking). Like all scientific terms, it should have neither positive nor negative connotations; but the implications of unspoiled innocence (for Huxley in Brave New World and Rousseau as previously mentioned, for example) or animal brutishness (in too many examples to name) make it too difficult to use objectively.