I'm trying to make some cuttings of a larger tree. The brown branches are way too thick to cut with pliers. Can I cut the young green part that doesn't have any brown or will that not root?

Pliers aren't the usual tool, although they will work.  According to the USDA green cuttings don't root as well as dormant cuttings but some people have a lot of success rooting green cuttings.  Perhaps a better way is to air layer your branch.  You can search on airlayer or air layer in this forum or on google to see how.

Hi Ogorodnitsa,
If you keep five centimeters of the brown wood, that should be enough.
Remove all the leaves except the 2 last tiny ones.
Rooting method is to your liking : At this time of the year, water or direct in dirt with frequent watering.
I started a test with green cuttings - pinching wastes from my crazy dalmatie tree2 -, and for now ( 14 days), they all are still healthy and this evening, I saw white dots on the stems ... Who knows, roots for next week perhaps...
So, if I were you I would try green cuttings in water . Replace the water every two days. When putting the new water in the container make bubbles :) - I don't know if that helps but ...

I use an air pump with air stones and it keeps green cuttings in great shape. Once you see white dots - any time after that they can be planted. I've planted as soon as I see white dots or after substantial roots have formed - and anywhere in between. I love green cuttings. I do keep the different cuttings in different containers and use aquarium valves to divert the air to different stones. Sometimes I have as many as 20 going at once.