Is the word cortar the same in Brazilian and European Portuguese?

No

While the fundamental meaning of "cortar" (to sever or slice) is identical in both dialects, the word is not "the same" because there are differences in typical usage and the grammatical structures often associated with it. In Brazil, "cortar" is frequently used to describe a disconnected phone call ("a ligação cortou"), whereas in Portugal, it is much more natural to say the call "fell" ("a chamada caiu"). Additionally, while both dialects use the verb, the surrounding grammar—such as the use of prepositions with "precisar" or reflexive pronoun placement—differs significantly.

Brazilian Portuguese Examples

1. Eu preciso cortar o cabelo amanhã. (I need to cut my hair tomorrow.)
2. Cuidado para não se cortar com a faca. (Be careful not to cut yourself with the knife.)
3. A ligação cortou do nada. (The call cut out out of nowhere.)
4. Ele cortou o assunto para evitar confusão. (He cut the subject/changed the subject to avoid confusion.)
5. O governo vai cortar os gastos públicos. (The government is going to cut public spending.)

Portuguese (Continental) Examples

1. Eu preciso de cortar o cabelo amanhã. (I need to cut my hair tomorrow.)
2. Tem cuidado para não te cortares com a faca. (Be careful not to cut yourself with the knife.)
3. A chamada caiu do nada. (The call dropped out of nowhere.)
4. Ele interrompeu o assunto para evitar confusão. (He interrupted the subject/conversation to avoid confusion.)
5. O governo vai reduzir os gastos públicos. (The government is going to reduce public spending.)