Mechanism of Action (MOA) refers to the effects of a drug on a molecular level (receptors, chemical reactions) and Mode of Action (MoA) to the effects on a functional or tissue level, which are more observable. So, actually, in most cases, we know how a drug works, because we can see its effects, but we may not know "how exactly" it works.
Wikipedia has a short list (far from complete) of 67 drugs with unknown mechanisms of action.
On DrugBank, you can see that mechanism of action for many drugs, including some very well known, such as ibuprofen, is "not known" or "not completely understood," etc. Despite that, the main effects of the approved drugs are known otherwise there would be no good reason to use them.
Even if the data about "mechanism of action" or "pharmacological action" are presented in detail on sites, like DrugBank, Drugs.com, DailyMed and RxList, you can't really search them in the way to find a "percent" of drugs with known or unknown mechanisms.