to play dumb, to act clueless
Não adianta dar uma de João sem braço, eu sei que foi você que comeu meu bolo!
Don't play dumb, I know it was you who ate my cake!
The image is of a man hiding an arm to seem unable. The common account traces it to people who feigned a missing limb — beggars simulating mutilation for alms, or men dodging labour and military service — pretending to be incapable rather than admit they simply would not do the work. João, the most ordinary Portuguese name, stands in for "any man".
Source: Ciberdúvidas da Língua Portuguesa.
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