I am not very informed in this subject. Whatever I know is based on casual observations.
LEGAL ASPECTS OF BANNING COW SLAUGHTER AT NATIONAL LEVEL
1) Some people run business of running slaughter houses. They claim that law to ban cow slaughter can infringe upon their fundamental rights guaranteed regarding doing business of one’s choice.
2) Some people say that in their Hindu religion, cow is worshipped like a mother. Therefore permitting cow slaughter is violative of their fundamental right of practicing religion of their own choice.
3) Thus the legal dispute is about seeking a balance between two conflicting fundamental rights.
Both sections are complaining violation of their fundamental rights.
The burden is on States and Center and Supreme Court to balance these rights and to pass proper laws.
There is concept of Reasonable Restrictions. All fundamental rights are subject to reasonable restrictions.
So there is a legal power in States and Center and Supreme Court to ban cow slaughter by putting reasonable restrictions.
Even without any law in this area, if cow slaughter is hurting religious sentiment of any religious group, they can consult local court lawyer about filing a complaint under Sec.200 to magistrate for offense of hurting religious sentiment.
Magistrate can then call report from police.
Link for laws on subject