Therefore, when 'Your disk is almost full' message pops up, you should check your current disk space and start to free up disk space on Mac. When disk is almost full, there are many observable markers like Mac will begin to operate really slow, Mac may crash in some instances, apps become slow to respond, and the system may become overheated. Bonus Tip: All-in-one Tool for Optimizing Your Mac.What Happens When the Disk Space is Full.