Cutting out patterns from felt is a little different from cutting them out of fabric. In this post, I will give some tips on how to transfer your patterns onto felt in order to cut them out neatly.
The first step in the process of cutting out a pattern from felt is to transfer your pattern onto the felt. But, unfortunately writing or drawing on felt is tricky. This is especially true if you want the markings to be temporary, which is often the case when tracing patterns onto felt. You can draw on felt with a tracing pencil or chalk, but I find that it is difficult to make accurate markings with them especially when the pattern is complicated.
So, instead of tracing patterns onto the felt, here are two ways that I use and recommend as alternatives.

The first method is to temporarily attach the paper pattern to the felt with tape. I use Scotch Magic Tape, which works really well and is easy to remove from the felt after cutting.

The other way is to trace the pattern in pencil onto freezer paper (drawing on the matt side!) and then iron (medium heat) the freezer paper pattern (matt side up) onto the felt. This way, the pattern itself is attached to the felt and is thus less likely to slide while cutting. Also, the freezer paper patterns can be reused several times!
Both of these methods work well, but one is better than the other depending on the complexity of the pattern that you want to cut. The taping method is quicker, but it relies more on your skill to cut accurately while keeping the pattern in place. The freezer paper method, on the other hand, requires more steps (i.e. tracing, cutting the freezer paper, and ironing) before you can start to cut out the patterns from felt. But, all that preparatory work makes the job of cutting a lot easier.
So, I recommend the taping method for fairly simple patterns and the freezer paper method for more complicated patterns.

Now that you have your pattern attached to your felt, you can start cutting! As for cutting tools, I have always used a smallish pair of very sharp scissors, like the one on the right in the image above. I recently experimented with a fingertip-grip swivel knife (shown on the left in the image above), thinking that it might make the cutting of detailed designs in felt easier. But I must report that it was not the case, at least for me.
I was able to cut felt with this mini swivel knife, and its swivel feature seemed to help with the cutting of curvy lines. But the blade was a bit too small for the thickness of the felt and therefore often did not make a clean cut the first time around. It also tended to catch on the edge of the pattern, either getting itself stuck or causing the cut to deviate from the intended edge as a result. Perhaps it would work better if the blade were bigger…

So, I am back to working with scissors. There are a few tricks to cutting out detailed patterns from felt. I share some tips in my post on how to cut out detailed designs from felt.
Lastly, in case you have not guessed, the curious pattern shown in the above images is a pair of antlers for the Huggable Reindeer, shown in the first photo. If you are interested in making your very own stuffed reindeer or any other of the Muumade animals, please visit my etsy shop for their patterns & instructions!
Hurray for felt crafting!