One thing to note is– an SSD will only fix stuttering if it's the hard drive causing you issues. If you notice that the issue is with framerates, then playing with your storage drives won't make any difference. GPU is responsible for framerates in games, so it is the GPU that causes framerates problem.

Can a slow SSD cause stuttering?

If you system has a mixture of SSD and HDD drives, the Paging file might be set on an a old or slow Hard Disk. This can cause stutter while swapping pages.

Does SSD make games run smoother?

The faster read and write times of an SSD help it load large files faster and also cut down on the boot times into both your operating system and the programs and applications on your computer. However, in terms of in-game performance, an SSD will not provide any kind of significant performance advantage.