Using part of zakat money for adha ((slaughtering sacrificial ram)) is not permissible because the zakat is the right of the poor. It must be paid to them.
The adha, according to most Islamic school of thoughts, is not obligatory. Whoever wants to make the sacrifice can do so, and whoever does not want to can leave it. There’s no harm in it, although it is better to make the sacrifice of adha if one is capable.