Theoretically you can eliminate metaphor, yes, but you are working against human nature itself.
Certain metaphors are exceedingly common and embedded in the very grammar of many languages (although their exact expression may vary), so in that regard, avoiding metaphor is extremely difficult because it's somewhat an inherent part of the human psyche. Either you will subconsciously integrate some of it, or your users will inevitably create some. Grammaticalization typically originates directly in widespread metaphor.
Your etymologies and extended meanings (because even in an auxlang, creating a root for every meaning is downright exhausting: there's a reason most auxlangs borrow at least part of their vocabulary!) are usually going to be metaphorical in some ways, whether from real languages or from otehr roots. Indeed, "metaphor" is an example: etymologically, the meaning is "carry over, transfer".
Up is good, down is bad, quality is possession (hence the use of "have" for qualities and actions), individuals are samples ("a human has two eyes" is metaphor: you don't mean a specific human!).
Time is a major source of metaphor in this regard. Time usually moves from back to front. Movement is the key word: verbs of movements are extremely common expressors of time relations!
The body is space: using body parts to generate locatives is also a very common feature cross-linguistically, found in languages as distinct as Hebrew, Nahuatl and Swahili. The fact that virtually all languages in the world use body-relative directional (in front of, behind)... except for the aboriginal language Guugu Yimithirr, well known for using only absolute directions.
Fabrication is causation: the use of verbs meaning "make, create, fabricate" as causative auxiliary is a common metaphoric transfer of the idea of creating an object to "creating" an action in something else.