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We extend to c{\`a}dl{\`a}g weak Dirichlet processes the C^{0,1}-functionalIt{\^o}-Dupire's formula of Bouchard, Loeper and Tan (2021). In particular, weprovide sufficient conditions under which a C^{0,1}-functional transformationof a special weak Dirichlet process remains a special weak Dirichlet process.As opposed to Bandini and Russo (2018) who considered the Markovian setting,our approach is not based on the approximation of the functional by smoothones, which turns out not to be available in the pathdependent case. We simplyuse a small-jumps cutting argument.

It{\^o}-Dupire's formula for C^{0,1}-functionals of c{\`a}dl{\`a}g weak Dirichlet processes