Why is plagiarism so harshly punished?

One key difference between plagiarism and violence is that plagiarism is a specifically academic offense, while violence is already handled by the legal system. If a violent incident is sufficiently serious, it can and should be dealt with in court. This means university rules only need to deal with cases in which the people involved prefer not to take legal action, and they can leave more serious cases to the legal system. In particular, the university rules are typically geared towards the less serious end, since those are the only cases they expect to handle. (If a student or colleague punched me in the face, I would press charges in court, rather than relying on the university to administer justice. By contrast, if two athletes got worked up and started fighting during a high-stakes game, it's possible that neither one would consider the incident worthy of legal action.)

Plagiarism is not always punished severely: a first offense or minor case may be treated leniently. However, the rules allow severe punishments because there are no courts to fall back on. By contrast, universities don't need to have special rules for how to punish a truly dangerous student.

An important part of the answer to your question is lurking in the "can" in your statement "plagiarism can easily mean being expelled or suspended." In fact, a first offense in plagiarism is likely to result in warnings, zero marks, and/or failure of a class rather than directly in the expulsion of a student, except for particularly egregious violations (e.g., plagiarizing one's thesis). Note, however, that particularly egregious theft or violence can get a student kicked out for a first offense as well (drugs aren't as good a comparison because many are dubious about considering them a significant offense in the first place).

So why is plagiarism considered an offense on the same scale as violence against another student? Like violence, it strikes at the foundation of the entire academic and scientific enterprise. The foundation of academia is production and dissemination of knowledge. Plagiarism undermines both, particularly since discovering one instance of plagiarism can cast doubt on all of a student's other work as well---is it original, or have they merely failed to yet find the source from which it was stolen? Likewise, since it is such a foundational and corrosive problem, an institution can be badly damaged by tolerating it or by gaining a reputation for tolerating it.

Thus, the zero tolerance policies and the potentially draconian punishments: one serious case of plagiarism can cast doubt on the entire history of a student's work, and tolerating plagiarism can form an existential threat to an academic or scientific institution.

One factor that I don't see in the other answers so far is that plagiarism is usually very hard to detect: if a student copies an answer from an obscure internet website or book, only a tool such as TurnItIn might be able to detect it; if they copy from a student in another section or from a previous year, they may only be caught if the same TA graded both sections; if they paid another student or TA to write an answer for them, it might be entirely undetectable unless someone confesses. A student may also plagiarize in multiple classes, and might get off because each of the teachers who catch them decide to let them off with a warning.

If punishment for plagiarism was lenient, students would be likelier to risk cheating, knowing that on the off chance they're caught, they'd only receive a minor punishment. Therefore, the punishment has to be harsh enough that students acting rationally realize that, even with a small chance of getting caught, the resulting punishment is severe enough to deter them from attempting it at all. (See Psychology of Academic Cheating, pg. 144 for a possibly clearer description of this problem).

My own approach to this is to scare my students at the start of the semester by telling them how seriously I take the slightest attempt at plagiarism, but then evaluating them on a case-by-case basis, and only sending the severest cases to my school's Honor Code Council.