As Barry pointed out, on the TC40DA, you should engage the PTO at low rpm to preserve the life of the PTO clutch/brake in the tractor. Also slowly feather the lever until the PTO clutch engages. Your tractor has so much torque that you'll likely break a shear pin on the mower if you just pull the lever even at low rpm.
When you get ready to disengage the PTO, slow the engine down to idle speed before disengaging. When you disengage the PTO brake will stop the mower spinning in about 5 seconds. If you have the mower at high rpm, it puts excessive stress on the PTO brake.
I have 1750 hours on my tractor and my PTO clutch and brake still work like new because I am very careful to follow the rules above. Once the mower is running, you can increase engine rpm up to 540 PTO speed as shown in the lower right portion of your instrument panel. A little green light that says "540" will illuminate when the engine is around 2600 rpm. If your mower cuts fine at a little below this rpm, it's okay to run slower, but not a lot slower. Rotary cutters are designed to run at 540 rpm and that's where they work best. Don't worry about your engine running that fast. It may take getting used to, but your engine will be fine running 2600 rpm.