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Won't your social security income be transferred into your Portugal  bank account?  Why would it be taxed?

Mine is deposited in a US bank and I choose to transfer funds or not.

Depends.

Are you a tourist?

Do you have a D7 visa?

Do you have NHR status?

Yes, it will be taxed unless you set up special provisions or qualify for tax-free or reduced tax programs in Portugal.

If you apply for Dual Tax status, however, you will not be taxed twice although you may be taxed the difference in rates if - most likely - there is a difference in tax rates between your home nation and Portugal

As the progressive tax rates are very high indeed, you may want to scrutinise your tax position closely in order to be faced with a major shock.

@Lynda Entzion

Portugal taxes its residents on a worldwide income basis - whether the income is remitted to Portugal or not. Some income streams might get some tax breaks in terms of domestice legislation, and other income streams might be reserved to the source country in terms of a double tax treaty such as 'civil' pensions (government pensions). Social security from the US can be taxed by both countries in terms of the treaty.

@bobinportugal22

If you are a resident, even if your foreign income is not remitted it is submject to tax in Portugal (subject to tax breaks and / or tax treaty 'breaks'). Whether the PT tax authority picks up non compliance is another mattter

@Lynda Entzion

Worldwide income is taxed on your resident country. So if you live in Portugal it will be taxed here.

The US has a double tax agreement with Portugal so you will only pay tax in Portugal, not in the US.