What if a man who testifies that there is no God but Allah and offers the Salah (prayer), but does not pay the Zakat?
Zakat is one of the pillars of Islam and if one gives it up, denying that it is obligatory, then its rulings should be explained to them. If however they still refuse to pay the Zakat they are considered to be a disbeliever and after they die, Funeral Prayer should not be offered for them nor should they be buried in the Muslim graveyards.
However, if one abandons paying Zakat out of miserliness while believing that it is a religious obligation, they will be committing a major sin, but they are not to be considered disbelievers. If they die in this case, their body should be washed and the Funeral Prayer should be offered for them, and Allah may punish or forgive them on the Day of Resurrection.
To make things clear, when a Muslim has the Nisab (minimum amount on which Zakat is due), it is unlawful for them to not to pay Zakat, even if they are in need of that money, as the need is not an excuse for refusing to pay the Zakat. This way, if it ever happens that one day they themselves are in need of money and deserve to be given Zakat, they can receive Zakat funds from others in a way that meets.