What can I use to glue acrylic sheet together?

If by Plexiglass you mean acrylic sheets, use acrylic cement. It formulated especially for that. Old way to dissolve small pieces of plastic in dichloroethan, but it is more toxic. Cut plastic easier than glass.

It's not always easier to cut plexiglass than glass.

I recently had to cut some (very expensive, stupid panicvirus) plexi for a project and had a dickens of a time with the score-and-snap method because the plexi was too flexible. I ended up cutting it with a circular saw.^*

If you have very stiff plexi, you can probably do the score-and-snap quite easily (I've done that before), just like you would with glass. If it's flexible plexi, it will be more difficult.

If you need complex shapes, especially curves, then the plexi may be easier to work with because you can use regular wood working tools to cut & shape it - just be prepared for the smell of melted plastic and work in a well ventilated area. You can cut complex shapes, even curves, into glass but it may be more work to do so - score-and-snap many short lines, then "sand" or grind the glass into the curved shape with an appropriate, hard sanding block, probably something specifically designed for working with glass.

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^* Make sure you wear eye protection if you're going to do this!! I had little pieces of plexi flying everywhere. I used a 6.25" battery powered circular saw with a home made track saw and just took my time to ensure that the cut was nice and clean. Man-o-man did the little pieces of plexi fly! I had several hit me in the face, though none cut/scratched me. I had a couple of pieces bounce off the safety glasses too. (Note that my saw seems to be designed to throw as much dust into the operators face as possible, YMMV.)