This is not plagiarism.
Plagiarism is taking credit for someone else's work. It is taking someone else's ideas and making the claim that they are the fruits of your own intellectual labor. Plagiarism can occur when one copies and pastes the precise words of another author without citation, but can also occur through paraphrasing without giving a proper reference.
Plagiarism is a major offense in academia, since those in academia live and die off of the ideas they produce. It is important in this setting that the people who first came up with an idea are properly credited, and that the entire chain of reasoning is laid out (since a flaw in a 50 year old paper by A. Adams might ripple down to preprint by Z. Zhang). We have to know where the ideas came from, hence there are strict cultural norms regarding citation and credit throughout the academy.
Good instruction will help students to understand these norms, and to inculcate them into the ethos of budding academics.
This is not cheating.
Assuming that students are copying and pasting in an appropriate manner—that is, they are not copying too much, are properly indicating which sections of material are direct quotes, and are correctly providing citations to the original work—they are not cheating. Indeed, this is standard practice in academic writing.
You are welcome to create your own rules for your assignments, such as insisting that students never copy-and-paste, but this is simply a standard which you would be setting in your own classroom. Failure to adhere to such a rule would not be cheating, and would only constitute a failure to complete the assignment as instructed (much as asserting that 2+2=5 would not be cheating—it would simply be incorrect).
The distinction here is that cheating typically requires some mens rea—in order to cheat, a student needs to know that what they are doing is immoral or unethical. But directly quoting another author (with appropriate citation) is not immoral or unethical. Indeed, it is a skill which we, as educators, should be teaching students to do correctly.
This is a bad policy.
There are at least two major consequence I see coming from this policy:
Students will get better at actually cheating. You have created a situation in which you are muddying the actual definition of plagiarism, while also teaching students the skills that they need to plagiarize more effectively without getting caught. Naive cheaters plagiarize by passing off direct quotes as their own work. Sophisticated cheaters learn to pass off paraphrased and uncited text as their own work. You are rewarding the sophisticated cheaters.
You are failing to actually teach students what "plagiarism" is. Real academic writing requires the incorporation of ideas which were originally thought up by others. Most academic writing is incremental, and builds slowly on previous work—it is very rare for anything completely original and revolutionary to be published (in my own field, even revolutionary work like that produced by Newton, Leibniz, Gauss, or Fourier built on the work of others). Good academic style quotes others when they phrase something better than anyone else, and gives credit where credit is due, but paraphrases and condenses when required. Students need to learn when to quote, when to paraphrase, and how to properly give credit in either case. Banning direct quotation fails to teach this skill, and muddies the waters around academic integrity and real plagiarim.
A better policy?
My guess (my hope?) is that the goal of such a policy is to prevent "patchwork papers", in which students write a paper by directly quoting several authors and contribute very little of their own analysis or original thought. If so, there are better ways of handling this. For example:
Set limits on direct quotes. Explain to students that they can (and probably should) directly quote earlier work from time-to-time, but that the bulk of their writing should be original. Set a limit on how much direct quoting they can incorporate into their work as part of your rubric. Making up numbers off the top of my head, something like "At least 90% of the words you turn in must be your own original writing."
Don't count quotes. If the assignment is supposed to be 500 words (or 50 pages, or whatever), don't count quoted text towards that word limit.
Grade drafts / allow revision. Keep in mind that the goal of any assignment should be to help students to learn or practice some skill (if your goal isn't helping students, you should consider another profession). Rather than having students put all of their eggs into the one basket of a final paper, collect and grade their work at important checkpoints—have them turn in a rough draft, and give feedback on that draft. This gives you an opportunity to point out excessive quoting before the final document is turned in, and gives you the chance to indicate how that rough document would be graded if it were turned in as a final draft.
In addition, as has been pointed out by several commenters (both below the question, and below this and other answers), excessive use of direct quotation is poor style. It isn't dishonest, or cheating, or plagiarizing—it is just bad writing. It is entirely reasonable to dock students points for bad writing, but it needs to be clear that this has nothing to do with "academic integrity" or "plagiarism". You are docking them points (or should be, anyway) because you are trying to teach them to be better writers, not because you are trying to punish them for violating academic ethics.
