No, this is not how it works in the majority of EU and west European countries with a few exceptions.
Each country has it own rules for if you are a tax resident or not, and most do not check if you are a tax resident elsewhere. You usually have to enter an address somewhere else though, but what matters is that you dont meet the criteria for tax residency - and just having a passport is typically not such a criteria.
Examples:
Ireland - you cant be in Ireland more than 30 days in the calendar year after︀ you leave Ireland, after that you can be up to half year in Ireland without︁ becoming tax resident, and you can still own property have bank accounts in Ireland etc.︂ You have to enter an address abroad (easily done online on revenue.ie), but Ireland will︃ not tax you unless you spend too much time in Ireland.
UK - similar to︄ Ireland, but multiple days tests. If you dont spend too much time living or working︅ in the UK, you are not a tax resident in the UK, regardless of having︆ a tax residency elsewhere or not (but you have to give an address abroad to︇ HMRC).
Italy - You have to register at AIRE (Registry of Italians living abroad) and︈ to do that you have to prove that you are a resident abroad which is︉ a simple formality normally, but in tax havens they make it more difficult. After having︊ registered with AIRE somewhere, you dont have to - in practice - be a tax︋ resident there, but if you are a high profile case, Italy could check that you︌ really dont have ties to Italy, and possibly - but Im not sure about this︍ - that you really live in the country you say you live in.
Sweden -︎ If you have significant ties to Sweden such as close family, permanent home, or a️ business, you are still considered tax resident in Sweden even if you live abroad. If you cut the ties, and dont spend more than like 3.5 months in Sweden, then you are not a tax resident in Sweden regardless of if you are a tax resident somewhere else or not (but you have to give an address abroad to the Swedish authorities).
Germany - Similar to Sweden but they have tougher criteria for the ties, included in the concept of habitual abode: access to a home (even if you just have a key but dont go there), a bank account, car ownership or gym membership︀ in Germany can matter.
Norway - This is an exception: For the first 3 calendar︁ years abroad you are still a tax resident in Norway but DTAs still apply. So︂ if you move a to a country with no DTA to Norway - tough luck!︃ After the 3 years it works like Sweden.
And notice that for Norway and most︄ other European countries it's not the Norwegian passport that matters, it's having been living in︅ Norway for at least 10 years - then you are in their tax net regardless︆ of citizenship, and the 3 years apply to you.
France - They have an exception︇ with Monaco, if you move there , your passport really works as a tie to︈ France, and you are still considered a tax resident in France no matter how long︉ you live in Monaco. For the rest of the world, I believe they check if︊ your center of vital interest is in France, and if it isnt you are not︋ a tax resident in France.