Whitecap, you should congratulate yourself on your intuition for English: indeed "excise" is a typographical error in the example passage.
By the way, native speakers frequently run into this same problem: they come across a passage where a word appears to be used wrongly, but they're not sure if it's just being used in a way they're not familiar with, or if the passage assumes they know some fact they're ignorant of. What a native speaker—and you—can do in a case like this is look up basic information about the topic. This is often much better information than is available in a general reference such as a dictionary. Of course, sometimes it's hard to know what information to look up, and usually the fastest method is to ask someone who's already familiar with the topic.
I'm a native American English speaker, but I've read a little about Westminster parliamentarism, so I can give you a brief explanation which provides some strong evidence that "excises" is a typo in the passage you found.
Quick explanation of Canadian government
In Canada, as in all nations that share the British Crown (that is, all nations that now have Queen Elizabeth II as their monarch), the Crown officially owns all the powers of government. That is, only the monarch has the authority to pass laws, to tax, to declare war, to hold elections, etc. However, by custom, the monarch only acts on advice officially received from her ministers, called "the government", who are elected by parliament. The members of parliament ("MPs") are chosen by democratic elections, and in practice the monarch plays a ceremonial role and sometimes helps opposing political factions work out compromises.
In the example passage, "the executive" refers to the government. Parliament as a whole, including members opposed to the government, regularly debate the government's policies, and at any moment can pass a motion of no confidence to remove the government from power, forcing the monarch to choose a new government (usually by holding elections).
In other words, the theory of Canadian government is that the monarch officially holds all legal authority but appoints a democratically elected executive government to exercise that authority on the monarch's behalf.