Which term describes a mild word used to replace a harsh or embarrassing word?

The term that describes a mild word used to replace a harsher or more embarrassing one is "euphemism." This linguistic device allows speakers to address sensitive topics in a way that is more palatable or less offensive to the audience. For instance, saying "passed away" instead of "died" is a common example of a euphemism.

Figurative language refers to artistic uses of language that go beyond the literal meaning, such as metaphors and similes, which do not specifically address the replacement of harsh words. Assonance is a poetic device involving the repetition of vowel sounds within words, serving a rhythmic purpose rather than mitigating harshness in terms. Archaism pertains to using outdated words or phrases that are no longer in common use, which does not relate to the aim of softening language for sensitivity. Thus, euphemism stands out as the correct term that specifically addresses the use of milder expressions in place of harsher ones.