Well, to begin with, that's a terrible misquotation of Aristotle.
What he actually wrote was the following:
But at present we are studying the best constitution, and this is the constitution under which the state would be happiest, and it has been stated before that happiness cannot be forthcoming without virtue; it is therefore clear from these considerations that in the most nobly constituted state, and the one that possesses men that are absolutely just, not merely just relatively to the principle that is the basis of the constitution, the citizens must not live a mechanic or a mercantile life (for such a life is ignoble and inimical to virtue), nor yet must those who are to be citizens in the best state be tillers of the soil（for leisure is needed both for the development of virtue and for active participation in politics.) -- Politics 1328b-1329a, Rackham trans.
So, the question then becomes: why is "a mechanic or a mercantile life...ignoble and inimical to virtue"?
Now, let us examine this a little more closely. By "a mechanic or mercantile life", Aristotle is talking about artisans and tradesmen; in fact, this is a common translation of the passage. And elsewhere in the Politics, Aristotle links artisans and tradesmen with "foreigners", describing them as being only slightly above slaves (1278a). They (artisans, tradesmen, and slaves) are collectively "servants to the community", but are not proper citizens-- which is the point of the main quote above. For Aristotle, citizens (properly constituted) should not be artisans, tradesmen, slaves or farmers-- because they lack the leisure time necessary for the cultivation of "virtue" (ἀρετή), sometimes translated as "excellence." As the linked article indicates, this is a key term for Aristotle-- the focus of his entire Ethics, among other things.
So, to close the circle: the point is not that "paid jobs absorb and degrade the mind"; rather, the point is that working too much takes valuable time away from more noble pursuits. Note that Aristotle here is being profoundly (and typically) anti-democratic; in today's terms, he'd be perfectly satisfied that the 99% are working so that the 1% can live a life of leisure, and there's no reason for him that the 99% should be citizens at all-- they are not the people that matter to Aristotle's state.
Since the question has been updated, I thought I would flesh out my answer a bit, to better match the concerns listed.
First, for Aristotle, the nature of the work isn't important-- it doesn't matter to him if you are a farmer, or a tradesman, or a soldier, or a craftsman. All are equally bad, in his opinion, and it has nothing to do with the nature of the work (repetitive or otherwise.) It's purely a function of time. If you are spending your entire day (every day) working, you're not going to have time to cultivate virtue.
This leads us to my second point: that any attempt to apply Aristotle's notion to contemporary society is hopelessly anachronistic. Aristotle was writing about a society that was significantly different than ours. The eight-hour day, and the five-day work-week are less than 150 years old. The notion of a liberal education, available to all, regardless of birth, is somewhat older than that, but not by much. The fact that you are able to read this (or anything) already places you far outside of Aristotle's conception of a worker. Aristotle's workers were largely illiterate, extremely uneducated, and had no time to take part in the pursuits of the mind that Aristotle thought were necessary for citizens. The same cannot be said for the working class of today, and even if it were the case, we are (generally) committed to a democratic ideal of citizenship for all that is inimical to Aristotle's views on society. At the same time, the democracy of Aristotle's time was a much more direct democracy, expecting the participation of all citizens in the process of governing (and not just through election of representatives).
A nice overview of Aristotle's political theory can be found here.