Which sentence is grammatically correct?

[Lingesh Kumaar]

Jack, ne mange pas ça
Or
Jack, ne mange pas ce.

Could you also explain why it is so?

Thank you.

[George Hunt]

Your first sentence is correct.

"ce" is an adjective . I think the grammatical term is a "demonstrative adjective".

As such (like all adjectives) we normally  need to have a noun that it refers to.

In your second sentence we expect a noun to follow "ce" but there is nothing and so the sentence does not "make sense". 

[Robert]

The pronoun "ce" can serve as object to a verb. But in that case it needs to be qualified in some way:

Jack, ne mange pas de ce qu'on a mis dans le bol à Lulu.

("Ça" on the other hand always implies some previously known qualification.)

[George Hunt]

Yes , I should not have said "ce" is (only) an adjective. It can also be used as a pronoun ,perhaps always as the  object to the verb (in which  case I think it needs to be followed by "que". )

I cannot think of any examples where it can be used as the subject of a verb.