Is there a reagents or mechanism that allows you to displace or get rid of a methyl group attached to a sp3 carbon like taking away the methyl group from methylcyclohexane? Of aromatics, my understanding is the methyl group in toulene cannot be removed because it would disrupt the benzene ring which is very stable/low energy 

Of course it can. In aromatic and aliphatic as well. One is oxidation with Permanganate to Carbonic acid and later change to Amid and use Hoffman reduction, Lossen or Curtius to Amin. And further reduction.

I just read potassium permanganate does not react with benzene or alkanes. You know I said cyclohexane not cyclohexaxene.  

Check here under number 6

 

https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Supplemental_Modules_(Organic_Chemistry)/Reactions/Oxidation_and_Reduction_Reactions/Oxidation_of_Organic_Molecules_by_KMnO4

KMnO4 is fine- if you have an aromatic ring, but the OP doesn't.

In principle you can dehydrogenate the methyl cyclohexane to toluene, oxidise that to benzoic acid, decarboxylate that to benzene and then hydrogenate it again to get cyclohexane.

 

But it's not easy or worthwhile.