Political violence was a very real threat throughout the late Republic, and even after the institution of military and quasi-military forces of order under the Principate violent demonstrations could and did appear. Violence was a useful tactic for a politician unable to force his legislation or suffering the dolor of an insult to his dignitas. Or sometimes it just popped up spontaneously when some condition was intolerable or an orator roused up a crowd out of control. Often violence was a mixture of the two, with leaders using small, private encourages to initiate violence around which larger mobs might rally spontaneously. A general survey of incidents of political violence is impossible here, but a good place to start is Lintott's Violence in Republican Rome, and probably Mouritsen's book on popular politics since I disagree with a lot of what Lintott says.

But yes, political violence was common in the late Republic. Was it, as you put it, a "staple?" I would say no, no more than civil war was a necessary card that Roman politicians had to play--sometimes, as during the tribunate of Sulpicius Rufus, the one led to the other. Political violence was generally a last-ditch effort, such as when the Gracchi resorted to it shortly before their deaths, or a means for determined forces to press an issue that they felt they could not win over any other way (I would argue Opimius, who threw the first punch against Gaius Gracchus, so to speak, thought of his violence like this). Political impasse could be broken in other ways. Cicero sincerely believed that his connections would defend him from Clodius' threat to exile him, and turned down his friends' suggestion that he turn to violence. This tactic seemed naive in hindsight, since Cicero was exiled, but it succeeded quite well for a while--it was only when Clodius broke his promise not to introduce a motion for exile and succeeded in getting Pompey to betray Cicero that the tactic failed. Plenty of other politicians did just fine in dire straits, or went down with the ship, without resorting to violence. We should see violence as one tactic in a politician's potential toolkit (and I mean all politicians, as an Opimius was just as likely to resort to violence as a Clodius) but not the only one. It could be, however, a devastatingly effective one if done correctly. At other times it might be totally disastrous--we're not sure whether Livius Drusus did employ violence to carry his Italian bill, but if he did his violent program was a total failure