Can augmentin (amoxicillin and clavulanate) cause severe fatigue and weakness?

Yes: Augmentin (amoxicillin and clavulanate) can change the microbial makeup of the GI tract and can lead to diarrhea and potentially loss of essential electrolytes, fluids and nutrients. These then can cause fatigue and weakness.

Not likely: Anything is possible, but this is highly improbable. The penicillins are among the least toxic medications you could be taking and severe fatigue and weakness is overwhelmingly more likely to be due to the underlying illness for which you are being treated.