males tend to get more terrtitorial as they grow , im taking it under the assumption you have a male because you used terms like he , him. this is normal behavoir for aging chameleons. what i would do is feed him a treat as you enter the cage like a wax worm or a butter worm or whatever you chameleon loves to eat. this should calm him down for a second so you can clean your cage
Inkys idea is good, you could also get a big plant like shleffara or ficus, and get him to climb out onto a stick and u can set him on the plant while you clean his cage.
Well, try to gain his trust, then he won't be as pissed. Hopefully.
The OP is getting a lot of good "canned" advise. It's all good in the long run, but doesn't really solve the immediate need. I'm not trying to be rude, but in the first example, a second or two distraction (if it works) may not be enough. The second advise given assumes he will respond to a stick. My Cham responds WORSE to a stick being put near him than if I put my hand in. Climbing on a stick that in turn will be carried by a massive human you are afraid of doesn't sound logical.
The third example makes perfect sense, but again this takes weeks to accomplish.
Here's my take, depending on what you need to do. You should define what your goal is and see if there is anything you can do to accomplish it with him still in the cage.
Example One (these were some of mine): I needed to trim some dead leaves off the plants in the back of his terrarium. My Cham got defensive as soon as my hand went in. I ignored him and he went to the opposite side of the terrarium and hide behind some leaves. I did what I needed and he (after throwing his fit) went his way and watched me.
Example Two: Misting. Up until recently, I had to hand mist every day and pick up standing water and poop. As soon as the door opened, my little Sherman ran for the hills after a show of anger. I once again ignored him and misted around him. Over the course of a week or two, he began to ignore the fact I was misting.
In the above two examples I not only did what I needed, but was also building the trust (even without food) that what I was doing was inconsequential to him and that I was not a threat.
Example Three: I needed to install a Mist King. I can't speak for all Chams, but my little Panther tries to climbs up and out when threatened. To install the Mist King, I needed to remove the top along with a lot of electrical stuff. I had no choice but to SLOWLY approach him with my hands cupped and when he ran to the mesh top, I very slowly and gently cupped my hands over him and even more gently closed them around him. When I felt he let go of the screen I enclosed him in my hands completely. He wasn't happy, he was very bright colored but NOT hissing or bloating up (perhaps due partially to the previous amount of exposure he has had to my hands being in his terrarium for maintenance) and I placed him in a box and closed it. I installed my Mist King (took about 30 minutes) and when I opened the box the instinct to climb out was there so he literately climbed out and went up my arm. I took advantage of this and handled him for a few minutes then placed him back in his terrarium.
Every situation is different. If your Cham hisses and bites, you may need leather gloves just to get near him. I have a female Veiled who hated everyone, even she learned to tolerate me being in the enclosure to clean up, but never became tame in the sense she never let me pick her up or hold her.