Elaine has a good point with the hand preference thing. Some scissors are made specifically for right handers or left handers. Some are made for either one.
When I was teaching we did a few of the following activities. The kids seemed to enjoy them, and they didn't realize that we were just trying to get them to cut.
Cutting out coupons (this is great for expired coupons or ones you’re not going to use, so it won’t matter if they get butchered-LOL! ) Plus, most have printed numbers, words, and pictures of the product so they can start making the connection between the product and and written name.
Cut the front labels off of cereal boxes, fast food bags, soup/vegetable can labels, etc. and make a collage or likes/dislikes.
Cutting up junk mail
Cutting out pictures from magazines, catalogs, etc. to make collages of things she likes. We did this a lot at Thanksgiving to talk about what we were thankful for, and also at Christmas as a Santa’s wishlist. You can do it as a classification exercise, too. Cut out items of clothing, things that are blue, animals, etc. I also did one where I used a paper plate and let them cut out pictures of foods that they liked and glues them on the paper plate.
Cutting out pictures from old greeting cards.
Draw a series of simple lines - straight, then zig-zag, then curvy and have her cut on those. After she’s mastered those, you can move on to cutting out shapes.
I have a list of websites with activities and worksheets for scissor skills. I'll try to find it and post it.