Since axolotls are critically endangered in the wild, it takes a special permit to import/export them in and out of Canada. Obviously, it’s also illegal to catch them in the wild (assuming there are any left!) But luckily for the survival of the species, axolotls breed readily in captivity.
Selling, buying, owning and breeding axolotls is legal through most of Canada — the notable exceptions are British Columbia and Prince-Edward-Island, due to BC’s erroneous classification of axolotls as wildlife, and PEI’s blanket prohibition of all amphibians (and confusion of axolotls with tiger salamanders, which are cousin species!) If you live in those areas, I encourage you to petition your local governments to have axolotls exempted from those restrictions.
Aside from this, you should check your city’s regulations before purchasing an axolotl. Some cities have weird pet regulations, and some restrict exotic animals altogether. Luckily, here in Montréal, all non-poisonous amphibians are allowed. Strangely enough, we need a permit to keep a cat or a dog!