Are you interested in coming to Japan? Or do you already have a flight ticket?
Travelling or living in Japan as a vegan is not impossible but not very easy either. It is quite difficult to find vegan / vegetarian meals on the menu of ordinary restaurants; I would say more than 90% of Japanese restaurants are not very aware of vegetarianism.
However, some of them would offer some vegan / options if you ask.
The problem is, most Japanese people are terrible at speaking in English, while many of us are rather better in reading. If you cannot make yourself understood in oral communication, try writing down the sentences you are saying; the waitperson might understand you.
He / she still doesn’t understand you? Try following expressions before giving up.
I am a vegetarian. I don’t eat any animal products. ==> 私はベジタリアンです。動物性の食品は一切食べません。
The word vegetarian (ベジタリアン or ヴェジタリアン) is already common in Japan (while there aren’t many vegetarians) but there are not many Japanese that understand what vegan (ビーガン or ヴィーガン) means. To avoid any misunderstanding, it is recommended that you describe yourself as carefully as possible. It is safer that you say “I am a vegetarian” and give details about what you eat and what you don’t eat than you just say “I am a vegan (私はヴィーガンです)” because the waitperson probably doesn’t know what vegan means.
I don’t eat any animal products, including fish, egg, milk and cheese. ==> 動物性の食品は一切食べません。魚や、卵や、ミルクやチーズも食べません。
As I mentioned above, it is safer you are as precise as possible. Many Japanese people think vegetarians eat fish and you will have to clarify that you don’t eat fish. It is better you say “milk and cheese” rather than you say “dairy products” (乳製品) because people sometimes don’t think much about the origin of milk and cheese are the same.
Could you please double check if the dish doesn’t contain fish stock, chicken extract and gelatin? ==> 魚の出汁やチキンエキス、ゼラチンが含まれていないかご確認いただけませんか？
Many people aren’t aware what gelatin is made from; it’s better that you mention you don’t take it. As you may know, fish stock is almost indispensable for traditional Japanese food. Some restaurants can offer dishes made with vegetable stock, but some would just decline you, knowing you don’t take fish stock. It isn’t because they are mean but it’s just because they believe they wouldn’t be able to serve the best dishes they could normally serve without fish stock. In this case, let’s forget about the restaurant and find another one. Chicken extract and pork extract (ポークエキス) are also often used with many dishes.
I hope these expressions would help you to make yourself understood.