Check that you've installed the right blades. There are blades that cut on the upward stroke and on the downward stroke. Downward cut blades will kick like crazy. Also make sure the perspex is supported as best as possible to stop it from trying to flex with the stroke of the jigsaw.
Have you checked the manual. My Dewalt Dws780 was not turning on, then I checked the manual and able to start it. There was some sort of plug issue with my saw but thankfully it sorted out quickly. I got this saw from this video recommendation.
Check your power supply. If you are using extension cords, they need to be 10-12 gauge wire. 12g or 14g are only good for 15 amps and no more than 50 feet. If you are using long cords and operating a 12 amp motor, you get a resistance drop that under powers the motor. This will eventually damage the motor and cause it to bog down. If the motor has brushes, check them for wear - if they are thin, you may need to replace them as well.
Most saws of this type plus many others need checking and if necessary calibrating when delivered and from time-to-time during use.
There are usually adjustable stops and often moveable scales so when checked against known accurate squares and angles suitable adjustments can be made. Sometimes the stops aren't adjustable and metal must be removed by filing or added by bonding a suitable shim.
One point of concern with many saws of the type is the position of the handle is often offset from the centre line of the pivot with the result; the force needed to overcome the resistance of the return spring is also offset and tends to twist the mechanism during the cut - the typical mechanism is not usually strong enough or built with sufficient precision to completely resist the twisting force which often results in a less than accurate cut even though the angle has been accurately set.
Knowing this the user can compensate by holding the handle differently or applying a twisting force in the opposite direction. With practice you will become familiar with the tool...