How to fix a counterweighted accordion blind that is stuck

If these are slatted miniblinds, each of the vertical strings goes down through the bottom rail and is held in place by a little button. Once you pop out those buttons with a small screwdriver, the strings are free and you can remove the bottom rail. Then you can un-thread the extra slats and re-thread the bottom rail back on, cut the strings and replace the buttons.

Honestly, vertical blind sets are so relatively inexpensive that if you've lost/broken this many slats I would seriously consider replacing the entire vertical blind. There are blind sets available from HIW stores as cheaply as $20. Even if you don't want to actually replace the whole thing, a kit like this is cheap enough to justify cannibalizing it for spare parts, so you could buy a cheap kit with the same color slats as what you already have, and just throw away the rail assembly, keeping the slats in storage for when more slats break (and they will; it's a guarantee).

As far as I have ever been able to tell, replacement vertical blind slats are not sold individually. Being made of vinyl, they have to be stored flat during shipping or else they'll never hang right; this makes packaging, stocking and selling replacement slats a bulkier proposition than you might think. Then, they have to keep a selection of popular color schemes in stock long after that color or pattern has been discontinued (a vertical blind set can last years if not abused, but those slats eventually WILL break up at the attachment to the rail, or split along their length when accidentally folded in half). All to sell them for maybe a dollar a slat. It just isn't worth it to the manufacturer or retailer.

As far as cutting to length, the default height for a vertical blind installation is that of the standard doorway, 84" (7 feet). You very rarely see vertical blinds in windows (though it can happen) and so there's less requirement for customization. However, any HIW should be able to cut vertical blinds to length using much the same equipment they'd use for cutting window blinds (if not the same method). I doubt though that they could customize the width of a blind set; unlike horizontal blinds such as for windows, vertical blinds have that bar mounted along the entire rail with bearings on both ends. You can't just lop some of that rail off and still expect it to work.