You can staple the top or use a whole bunch
Is the part that's broken is where the blinds are clipped for hanging? If so yhis maybe repaired by using one of two methods or a combo of both.
1. Use a colour matching duct tape patch. Cut a piece of tape large enough to start on one side and tape over onto the otherside. With pointy tipped scissors (or a hole punch) make a small hole big enough for the clip can hold the strip.
2. If you need some reinforcement, expoxy a bread bag tag to the spot on the wrong side.
3. The combo of bothwould be duct taping the tag. Most vertical blinds comes with a valance and would cover the tape if an exact colour could not be found.
Home Depot sells replacement blades
Is the balance broken? Or are the first couple of slats at the top broke it? If the balance is broken you might be able just to order another one and attach it
We have rental property so things don't always get the gentle usage we give our own things. I have done an easy repair by cutting a clear strip of plastic (clear water bottle works well) the width of the louver and tall just enough to come to the broken keyhole edge. Then I staple it to the back side and you are "good as new".