I have a hp mini. Lately it just cuts off mid stream whether it is plugged in with adapter or fully powered battery. Help

If system is shutting off and staying off, then mostly likely the CPU is overheating due to dust buildup on the CPU fan cooler or the thermal grease that goes between the CPU and the CPU heat sink is dried causing the CPU to overheat and shut your computer down to prevent further damage.
If system is shutting down then restarting on its own then it not an overheating issue. It could be hard drive issue; bad sectors on hard drives make your computer blue screen then quickly turn off, then rebooting the system.
Also your ram needs to be checked/ bad RAM will shut you down.
Let me know exactly what happens when it shuts down and I can help you further.