"The man speaks Swedish, but not the woman."
Translation:Mannen talar svenska, men inte kvinnan.
Det är inte en hund, utan en en kyckling. - It is not a dog, but a chicken.
Jag talar inte svenska utan franska. - I do not speak Swedish but French.
Jag ska inte spela baseboll utan springa. - I am not going to play baseball but run.
Negation first with inte, positive statement about what is instead with utan.
You would be understood of course, but it is a kind of 'false friend'; I believe English prefer 'speak' when it comes to knowledge of a language, Swedish prefer 'talar'. But when it comes to 'talk" (chatting), Swedish more often use 'pratar' or the colloquial 'snackar'. So I would say that 'talar' is a false friend of 'talk'