Is the following wording okay?
He can not only do this, but also do that.
In this case, it seems that the writer is dividing 'cannot' into two words. Is that acceptable?
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"Can not" is the original form, "cannot" and "can't" being contractions; all three are acceptable when referring to someone's inability to do something. However, in the sentence you quote, "not" modifies "only" rather than "can" so the contractions can not (or cannot or can't) be used. This becomes clearer if the sentence is changed to "He can do not only this but also that". You will notice that "not" changes place along with "only" rather than remaining next to "can".
In case if can not is used as two separate words as above,it's okay!! But it's not appropriate to use "do "again in the second sentence.