Is there a natural language w/ no morphology (i.e. one that has neither inflectional nor derivational morphology -- in other words, no affixation whatsoever)? I've heard claims to the effect, but the (admittedly very few) candidates that I've looked at (viz. Yoruba, Cantonese, Vietnamese) still have some (either inflectional or derivational) morphology
Vietnamese has no affixation at all, though it does have syntax. New words can (in principle) be formed out of thin air, or borrowed from other languages: so word-formation is possible in Vietnamese, and many people equate morphology with "word-formation" (I don't: I use "morphology" only to refer to grammatical word formation). There is also reduplication, which is a kind of morphology i.e. it is in the grammar (as are ablaut, process, and prosodic-pattern means of word-formation), so Vietnamese may not be the language that you are looking for, depending on whether you really depend on "affixation" as the distinguishing criterion.
The Chadic language Angas might come a little closer to having no morphology. It has two things that are just floating tones, which appear at the end of certain phrases in certain syntactic contexts (for example, an NP before a VP, a direct object NP before an indirect object). What is being marked is a grammatical relationship between higher-level phrases, and not some property of particular words. Syntactically, this is usually treated as the concatenation of a phrase-final marker and whatever word cones before it. However, it is phonetically realized as a change in the tone of whatever precedes it. So this could simply be syntax (positioning of a marker) plus phonology (realization of a floating tone within another word), and not morphology.
In other words, it depends on what your criteria are for calling something "morphology".
I have a feeling that this question has been asked somewhere, or maybe it's about monosyllabic languages. Anyways, while modern Mandarin Chinese is less isolating and indeed has words consisting of multiple syllables/with parts tucked on to some sort of inflectional effect (e.g. "-了" which is similar to the past tense inflection in English), the Classical Chinese is supposed to be purely isolating, i.e. each syllable in the text strictly forms a meaning unit, and there is no inflectional affixation whatsoever, if that's what you're looking for.
Note that this doesn't necessarily mean that the oral languages of ancient China were purely isolating. Classical Chinese is more of a written form for formal documents/historical records etc. It's suggested that people could have spoken in a quite different way compared with how they wrote documents, or they could have pronounced what seems to be one character with multiple syllables, at least people of different regions. However this can hardly be corroborated.
Also note that if you're wondering about "derivational morphology", then the way new words are derived in Classical Chinese is by combining a radical with a phonetic component. IMO this is just another form of derivational morphology, however from the perspectives of linguists who view the whole radical component + phonetic component as one single "character", of course this cannot be morphology since morphology must occur across multiple characters/syllables. The whole idea of morphology is very much centered on western languages and when applied to ideographic languages there can be problems.