WRT motive, the fact of whether it was or wasn't beef when introduced into evidence may prove to be exculpatory (if the finders of fact decide that it was justified) or may prove to be further damning (if the finders of facts decide that it was pre-meditated). I wouldn't want the police on the scene to be in the business of deciding what possibly relevant facts in the case will prove to be crucial. Collect, catalog, and preserve the evidence as best you reasonably can in a major crime case, and let the court system figure out what's relevant.
Additionally, if it was beef, there's a reason to look upstream to where the dead man got the beef and chase down those leads.
What's the external/societal cost to them taking the meat to the lab? It's not like the police not taking the beef to the lab will suddenly summon the cow back to life nor that they took the beef and tested it by eating it.
(I'm assuming from context that beef for consumption is locally illegal. That seems a safe assumption.)