It can. The hard drive should be used for storage mostly. Especially for stuff you don't need regular access to like photos,music and media.
The main operating system and your most accessed stuff should be on the SSD so it can take advantage of the increased speed.
But it sounds like your setup is actually the other way around.
If you were running your computer on an HDD and then later added an SSD the SSD will just be extra storage but your operating system and programs will still be on the HDD.
The HDD in this case is most likely acting as a bottleneck and slowing the system.