I would like to say: "The beef is a source." instead of being more precise and say "The beef is a source of meat." We can do that even if it sounds awkward right, as it is just imprecise, but still correct?
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"The beef is a source" would be extrememly confusing. Even "The beef is a source of meat" is awkward. Beef is not "a source of meat." Beef is meat. You could say "Cattle are a source of meat" or "the cow is a source of meat." But just saying "the cow is a source" would be very strange. I'm really not sure what you are trying to say.
Regardless that it is strange, we can still say "the cow is a source" right?
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You would need to say "The Beef is a source of meat.", but this is not quite right: beef is a type of meat, not a source of meat.

You could say "Cattle are a source of meat".

"Cattle are/Beef is a source." is unlikely but theoretically possible when the thing it's a source of has just been mentioned. For example:

You need to make sure you get enough vitamin X. Beef is a source.
Isn't saying "Cattle is a source." instead of "Cattle is a source of meat." exactly like saying "Having sex is an act." instead of "Having sex is an act of passion."?

Why can't we merely say "Cattle is a source"?????
A source has to be a source of something. As I mentioned, if that something is apparent from context then "X is/are a source." is possible. This tends to sound a bit abrupt, though, so it's more usual to say what it's a source of in the same sentence, either explicitly or using a pronoun such as "this".

It should be "Cattle are..."

Incidentally, "Having sex is an act" would also be a relatively unusual thing to say (though not wrong). "Act" is such a general word that it's almost a pointless and content-free thing to say (except if a specialised meaning of "act", such as "pretence", is meant, which I don't think is your intention).
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What? Can't we say either cattle are or cattle is?
"Cattle" is plural.
Ok, so we can't say the beef are a source of meat?
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