If a Canadian citizen commits a crime against another Canadian in the USA and Canada, can that person be arrested and prosecuted in both Canada and the USA?
If a person commits crimes in one country and then goes to another, the first country can ask the second to extradite the fugitive back to the first country. This is heavily dependent on international relations, but USA and Canada have an Extradition Treaty. Whether or not a person will be extradited may also depend on the severity of the crime.
A person could be tried in the United States or Canada and then extradited to the other country once they were acquitted or served their sentence. The first jurisdiction could even decline to try the person and instead just extradite them - a lot of this depends on the Attorney Generals/District Attorneys in the applicable jurisdictions. One other confounding factor may be applicable statutes of limitations, which may expire on one crime if the person serves a sentence for the other.
Usually, whoever got their hands on the defendant first would have first crack at it. The second jurisdiction would commonly not prosecute provided that justice was done in the first but they can - double jeopardy is not in play as a bar as they are different legal systems but courts usually apply the spirit that a person shouldn’t be punished twice for the same act.