You never want to pull your material off the mat. Use a spatula or thin credit card or something like that to break the adhesive bond and it will come off beautifully. I have removed tissue paper without it tearing - but you have to just loosen it first. And yes - you will have little pieces that were cut out stuck on the mat - that is the beauty of it - just scrape them off onto the spatula and toss them out or hold the mat over the trash can and push them off that way. I usually just scoop them up and throw them out. The beauty of the pieces staying is, depending on the design. you can pull them off and have another image that is the negative of what you just cut, depending on what the image is.
As stated all through the forum, you can also use a cotton t-shirt or cloth to blot some of the sticky off (personally I love it sticky but some do not). But I still always use a small spatula to remove my projects.
The print and cut is explained in the learning center. There is also an excellent video on it in the webinar section under broadcasts. You are a very new user based on when you joined the forum, and we don't recommend jumping into print and cut this early because it does take a good basic knowledge of the machine. Take it slow.
And I know 7-8 hours may seem like a lot of time, but it really isn't. Just work through the steps slowly and it will all come together. It just takes time. Go for the little successes first and build on those. It will save a lot of frustration down the line. Good luck.
Here is the link to the print and cut video when you are ready.
viewtopic.php?f=54&t=5837#p94824