Could be an overheating issue. Download HWMonitor / CPUTemp or similar and post your temperatures. Also make a check inside your PC that anything isn't badly seated. For example I incorrectly seated my CPU cooler and had these low fps / fps spike problems.
If this turns out to be the problem, buy a bigger heatsink or thermal paste instead of using the CPU's own stock cooler, it can actually crack up pretty easily.
Also there could be a possibility your hardware isn't getting the required voltage. Take a look if your power supply actually offers the amount that is needed.
Similar issue could be that your GPU is bottlenecking CPU or vice versa.
Post your PC specifications here. Helps a lot
It's pretty rare that any of these problems are software-based, but there is a possibility. Do a virus scan, CCleaner, check your task manager during gaming for disruptive process etc.
