Yes losing too much blood when on your period can make you feel dizzy.
When you lose too much blood when on your period it causes a temporary drop in your blood pressure which can then lead to the dizzy feeling.
Just like if you get cut and lose blood from the cut you can feel dizzy and faint.
I remember one time when I was 8 years old I got cut on the head and I was losing some blood and I was okay for awhile but then I got dizzy and fell to the floor.
My mom called an ambulance but luckily I was okay but they took me to the hospital just to be safe.
When you lose some blood then the pressure in your blood vessels drop which causes dizziness.
Just like if you have a leak in a water pipe or air hose etc the pressure drops.