How Do You Remove CD Booklet/Artwork?

Depends how thick the insert is, and I'm guessing for this question it's one of those thicker booklets. For me I lift up the right side, the side that's bound, then guide it up and out. Right side is the safest as you won't have any pages potentially snagging on one of those clips. Maybe fashion a tool to help lift it out? 

Thank you, everyone!

Holding the CD case in your left hand, just gently place the tips of the fingernails of your right hand under the last page of the booklet and carefully lift it out of the case. When that doesn't work, apply more pressure to the underside of the case, introducing a little bend in the plastic case and lift the booklet. When that doesn't work, remove the CD from the case and set it aside. Now, place one toe under the bottom of the case, and the heel of the other foot on top of the case, and just smash the holy bejeezes out of the entire thing. Then separate the broken pieces, remove the booklet, read it, then put it back into a brand new Jewell case. Case solved.

Frank

A common problem. Worse yet, the jewel case always ends up falling on the floor eventually and cracking; or the hinge tabs break off. Terrible design. And don't even talk about double CD cases!

I just pop out the entire insert. Gently of course. Once you realize how they are put together it is easy to take apart and reassemble without damage.

Jackhammers will do the job. 

I usually take a sledge to it, and if that doesn't work, a flamethrower.  

Small pocket knife, or a butter knife, insert at center of booklet, slightly lift center of booklet, this will allow for safe removal of book, without the usual pushing and causing tab dents.

I replaced the hard plastic boxes for soft plastic envelopes. Takes up about 80% less space in a dedicated 'drawer' filing system (I have an excessive amount of CD's).  The envelope has has pockets on each of it two sides,one for the disc the other for the CD Booklet. It also hgas a space on the top edge of the disc Id taken from the side of the CD Case insert. I file them just as you would find them in an old record store and its fun to look thru them and see all of the covers, not just hard to read side labels. 

This is very terrible buy LPs instead there easy to open and sound better.

Just be careful. What I do is gently pry it out with my fingernail without putting pressure on it to move while doing it. Once freed, a gentle kind of shake after doing that works for me. You want it to move back a bit  away from the ridge after getting a hold of it and then it slides out real easy.

All the best,
Nonoise