If you put your mini to sleep, it should continue to sleep, until you wake it, or something disturbs that sleep, such as plugging/unplugging a USB device, or accidentally pressing a random key on your keyboard - unless your mini is set to go to a deeper hybernation mode, when your mini might appear to power off completely. (Off, but restores back to current state after pressing and releasing the power button) That deep sleep mode is probably unusual, if that's what you see.
-- So, depends on what you are doing, and the power settings that you might have in use, and also depends on the rest of your hardware configuration, particularly what kind of external devices you would have attached.
AFAIK, if your mini is a 2018 or later model, there is no indication light for sleep mode, like there is on older Macs -- so there is no visual indicator that your Mac is sleeping, other than the display would be black. The power light will always be on, unless your Mac power is off. The power LED remains on, even when sleeping.
Are you having any kind of problem? Which mini do you have?