Roman Law worked just like law today (minus the fact that their punishment would be unusual today). For criminal proceedings, a jury of citizens, made up of senators and "high standing" people in the community would be selected as the jury. the accused had the right to bring in witnesses, and other defenses, Etc. A Roman citizen could only get a death sentence for one crime though, Treason. The other punishments were slavery, beatings, fines, and retaliation. What you mentioned is not legal under Roman law, though there is corruption in any system, so for senators they probably could get away with that for minor citizens. But under the Roman system, a slave owner could kill his slaves. Even slaves had protection though; You could be fined and beaten for killing another man's slave.
Edit: Roman citizens themselves could not be tried by a magistrate because only a full court could try a Roman citizen for any crime that could warrant capital punishment or the heavier fines; Roman citizens also had the right to be shipped back to Rome to get a trial and even those guilty of treason could not be crucified to death- they were beheaded instead. For the charge of Patricide, the person killing their father could not be a Roman citizen, at least not in relationship to their father. Because under Roman law, essentially all members of the family were legally almost slaves of the father (they could not own or buy property with the father's consent, or get married, or leave the household, and the father had the right to kill them for any punishment, imprison them, and sell them as slaves to anyone else, as well as banishing them from the country.). So it is hard for most people to conceptualize but the Father or Husband was the only one in the Family that could hold citizenship, usually, (once Roman citizenhood was expanded past Rome, the local provinces and tradition affected who officially had Roman citizenship or rights) and so he was responsible to make sure his family did not break the law, but he was the only one who had full protection legally. This made it easier for the people they viewed as the most trouble to be tried before a magistrate and be executed, such as women and foreigners.
California State University
Rights of Roman Citizenship