I will be cutting some dried maple branches (cut last December) up to 3.5 inches in diameter. I have cut some already on my table saw and the 60 tooth carbide gives a fair cut, but not smooth as glass. If I get a fancy 120 tooth blade or a good brand will the cut be smoother? I will be using a miter saw for the cutting.

Do you mean cross cutting? Or ripping? It makes a huge difference in what blade to use. A 60 tooth blade is on the border for ripping in my opinion. It should be plenty smooth for either operation. My real concern is ripping round stock on the table saw which is not safe unless the rounds are secured in a jig to keep them from rotating.

What is your method and plan for "cutting" these?

Well, since the OP stated he would be using a miter saw to make the cuts..............

A good quality high tooth count blade with a negative hook will give you a glass smooth cut. All the blades I use on my miter saws are a minimum of 100 tooth. Try to avoid thin kerf blades as they flex too much and degrade the cut. I prefer Amana blades, higher cost but well made and extremely accurate.

What will the finish product be? You can't really expect any saw to cut smooth as glass. This would only come from sanding so the blade would only make a marginal difference.

I was not reading the entire post, including the last sentence since "table saw" was in the title and he had used a "table saw" for some of the cuts. I don't understand why it's necessary for not quite "smooth as glass" on the end grain and that's why I asked what's the plan and method. I agree that a full kerf blade will give a smoother cut than a thin kerf which would flex under stress.

Sorry, I am back in to working with wood after 40 years. I should have specified a circular saw blade for cross cuts. I will be hopefully cutting many 1/4 inch slices from the maple branches I put in the barn last December. They will be used for a Lions Club kid's program to let the kids make rustic christmas tree ornaments. We will have rubber stamps for the kids to use to put designs on or they can use markers and paints. I was concerned about the possibility of the rubber stamp ink bleeding out, so I tried one of my office stamps on a few of the slices cut on my table saw. The surface was smoother than new unpainted dry wall and the ink did not bleed. (I want to eliminate sanding from the prep process) The club is having a DIY holiday decoration sale. We sell greens, pine cones, holly and other rustic items for the customers to make their own decorations for at home. The slices will also be for sale there too with a few of them decorated with wood burned, scroll sawed and other designs to show what can be done.

Incidentally, I think I figured out how to attach an air compressor hose to a miter saw so I can blow the cut branch slice away from the blade as soon as it is cut so there will be no reaching for the piece or need to turn the saw off and wait for the blade to stop each time. I think if I direct it right, the slices will be pushed into a bin by the air pressure. I will clamp a stop on the fence to make each piece uniform in thickness.

The smoothest cutting blade I have used, is a Ridgid 90 tooth blade. The model number is worn off, but the last numbers are 90C, and it says, Ultimate Polished Finish. It really left a polished edge. Much smoother than I need for 95% of the cuts I make, so I keep it for when it's needed.
I don't have, or used any designer hi dollar blades to compare to, but I can't see how a smoother cut is possible.
I read somewhere that it was made by Freud.
I got it from a Craftsman ras, I bought to send the motor in for the $100 bounty.
Here is a link to the same blade, but 12" https://www.amazon.com/gp/product/B0...=projectwp1-20