I just got my Cricut and it seems to be tearing all of my paper. But it's a new mat and new blade. Is anyone else having this problem and have any suggestions?

You need to check out your settings for blade depth, Pressure and Speed. It sounds like you are having an issue with those.

I have the Expression and here are the guidelines depending on what type of paper you are cutting (This is from my manual):
Adjusting Blade Depth
You will need to remove the cutting blade assembly from the Cricut™ machine before
you change the setting on the Adjustment Knob.
To remove the cutting blade assembly (Figure 1), locate the thumbscrew and turn it
counterclockwise until it loosens enough that you can swing the thumbscrew to the
right (Figure 2). Be careful not to loosen the screw too much, or it will fall out. Remove
the cutting blade assembly from the machine. Next, locate the Adjustment Knob (Figure 3)
on the top of the cutting blade assembly, and turn it to your desired setting (see the
paragraph below).
The smaller the number, the shorter the blade depth. Shorter blade depths are recommended
for lighter weight materials such as vellum, longer blade lengths for heavier
materials such as heavy cardstock. Reinstall the cutting blade assembly into the Cricut™
machine by reversing the procedure to remove the cutting blade assembly. Test the setting
on a scrap piece of paper and make adjustments as necessary.
Speed Dial
The Speed Dial allows you to control the cutting
speed for an optimal cut on a variety of papers.
If you regularly cut on thicker papers or cardstock,
you may want to turn the dial up to
increase the cutting speed. For lighter papers
such as vellum, or for smaller, more detailed
cuts, you may want to turn the dial down to
decrease the cutting speed. After each adjustment,
we recommend that you test the setting
with a scrap piece of paper, readjusting as necessary
until you achieve the desired results.
14
TIP: Cutting on cardstock and other heavy materials will reduce the life of your blade,
but it will produce the best cuts.
Figure 1 Figure 2 Figure 3
Adjustment Knob
WARNING! Always unplug your Cricut™ machine before removing the cutting blade
assembly!
15
The LCD screen will indicate the speed level, and the window next to the
dial will display an indicator band that becomes thicker when the speed is
increased and thinner with the speed is decreased. As a general rule, decrease
the cutting speed if your cuts are being torn. If this doesn’t work, the blade
depth may need to be adjusted (see page 14).
Pressure Dial
The Pressure Dial allows you to control how hard
the cutting mechanism presses against the
paper. For thicker papers, you may want to move
the dial up to increase the cut pressure. For
lighter papers such as vellum, you may want to
turn the dial down to decrease the pressure.
After each adjustment, we recommend that you
test the setting with a scrap piece of paper,
readjusting as necessary until you achieve the
desired results. The LCD screen will indicate the
pressure level and the window next to the dial
will display an indicator band that becomes thicker when the pressure is increased and
thinner when the pressure is decreased. As a general rule, increase the pressure if your
selections are not being cut completely through the paper. If this doesn’t work, the
blade depth may need to be adjusted (see page 14).
Pressure Adjustment Chart
LCD Screen Pressure/Material
Max Extra firm for heavy cardstock
High Firm for cardstock, textured, high fiber content papers
Med Factory default setting for printed papers
Low For lightweight papers
Min Light for vellum

Hope that helps, if not email me and I'd be happy to help.