That patient merit of the unworthy takes,
In this case, 'of' means 'from'.
(1) Put the words of the verse into usual prose order: the spurns that patient merit takes of the unworthy.
(2) Convert to clearer wording: the insults which the hard-working, patient person receives from the one who does not deserve credit.
Suppose you work hard at a project and make it succeed. Suppose your manager takes the credit for what you have done. Let us say you try to express in a meeting some of the effort you had put in. Now the manager says something like, 'You're working too hard. We need people who can deliver without taking all that time'. Let us suppose you do not return his comment in kind, but put up with it for the sake of avoiding confrontation.
This final insult after he has taken the credit is the spurn which patient merit (the hard-working, long-suffering person) receives from the unworthy (the type who rides to success on your back and then treats you with contempt).