What term refers to a mild or inoffensive word or phrase substituted for one that may be considered harsh or blunt?

The correct term for a mild or inoffensive word or phrase that is used in place of one that may be considered harsh or blunt is a euphemism. Euphemisms serve to soften the impact of the expression and make uncomfortable or awkward subjects more palatable in conversation. For example, saying "passed away" instead of "died" is a common use of euphemism to convey the same idea with greater sensitivity.

Metaphor, on the other hand, is a figure of speech that implies a comparison between two unlike things without using "like" or "as," thus it does not serve the same purpose of softening language. Hyperbole refers to exaggerated statements not meant to be taken literally, which again does not align with the concept of substituting a softer term. A simile is also a figure of speech that makes a comparison, but it does so explicitly using "like" or "as" and does not fulfill the function of a euphemism.