Can I get vegan sushi in Tokyo?

Only barely. Vegetarianism in general and veganism in particular is very poorly understood in Japan, and this r/japan thread goes into gruesome detail on what a world of pain you're about to find yourself in.The one vegetarian sushi place I'm aware of in Tokyo (Potager) has now closed.

The only vegan items you are likely to encounter in the average sushi shop are kappa-maki (?????), cucumber rolls, and natto-maki (????), fermented soybean rolls. The latter is an... acquired taste.

The other vegetarian-ish items you're likely to encounter are inarizushi (sushi rice in deep-fried tofu pockets), ume (Japanese plum), takuan (pickled radish) and kanpyo (pickled gourd), but these are more often than not prepared with dashi, the bonito stock that makes its way into everything in Japanese food, including (sometimes) the soy sauce you dip your sushi into. Good luck asking the chef if he knows what went into those as well: the vast majority of sushi places focus squarely on fish and buy ingredients for side dishes like these ready-made, and since dietary restrictions aren't really a "thing" in Japan, he's unlikely have had to research this previously either.

And that's about it. "Vegetarian rolls" and such — hell, rolls containing more than one ingredient in general — are unknown in Japan. Customers requesting items not on the menu or alterations to items that are on the menu are generally regarded as meiwaku (a nuisance), not a "fun challenge". That said, if you're going to try this in Japan, a sushi counter where you're sitting in front of the chef is among the less bad options; at least you don't need to play a game of telephone with the waitress and the kitchen.

You (as well as PLL, who commented and RoboKaren, who answered) need to straighten the confusion here. On the one hand, there is "sushi" (let's call this sushi1), which is an American food, hinted from Japanese cuisine and originated in California, and is usually served by Korean-Americans, Chinese-Americans, or other Americans. It uses normal rice, and is sometimes rolled with seaweed inside-out, has sesame toppings, and has stuffings like avocado, mayonaise, imitated crab meat, flaked tuna, etc. On the other hand, there is Japanese food ??, which can be transcribed as "sushi" (let's call this sushi2), which mostly is a piece of sea product, typically tuna, squid, salmon caviar, etc, on a small chunk of vinegared rice.

If you are talking about sushi1, then this is where you can expect vegan food, but you have no luck in Japan. Restaurants that serve sushi1 are rare in Japan. You will have hard time finding one.

If you are talking about sushi2, then you will see this all over the place in Japan (the best ones located in a neighborhood of a port), but the whole idea of sushi2 is eating sea products, mostly fish. If you are expecting a "vegan sushi2," that is almost self-contradictory. There are some vegan things like cucumber, but that should be considered as the minor part of the cuisine. Going to a sushi2 restaurant and keep eating only cucumber is like going to a hamburger shop and ordering pickles without hamburger, or going to a steak house and ordering fried potatoes without meat. It not only does not make sense, but it can be taken as rude and offensive to the shop.

You should not take this to mean that there are no vegans or vegetarians in Japan. Although its concept is not as wide spread in present Japan as in the Western world, there are such people in Japan. However, if you are a vegan, then choosing to go to a sushi2 restaurant in Japan is definitely a wrong idea. There are other kinds of vegetarian/vegan restaurants.