I got a puncture on my mtb and so I went to change it (I haven't had a puncture on this bike yet). I took the wheel off the bike and then went to take the tyre off, however the tyre is very stuck, I snapped a park tool tyre lever doing it. I still haven't managed to get the tyre off. The tyres are nobby nics. Any suggestion on how to get it off and why it is so tight?
Some tire/rim combinations are just inherently tight: if the tire is on the small side of the manufacturing tolerances, and the rim is on the large side, it's going to be tough. Some manufacturers do this intentionally to increase safety.
Also, some tire levers aren't great. I've got some Park-branded tire levers that are pretty useless; my current favorites are from Pedro's: they're much bigger (more leverage) and more rigid.
The usual trick with tight tires is to force the bead into the center of the rim, which normally has a smaller diameter than the edges of the rim. This gives you a little extra margin to work with, so you can "pop" the bead at the 12:00 position with the bead in the central trough at the 6:00 position. You may need speed clamps, toe straps, or an extra set of hands to hold things in place while you do this.
Of course, that's only half the battle. You'll need to get the tire back on at some point. For that, a tire jack can be essential. Also, using the same trick of moving the beads into the central trough before popping the last bit of bead on.
I suspect you have tubeless rims? and that they are the UST standard. WTB are a popular wheel brand using this standard for example.
You need to push the tyre bead into the centre of the rim in order to get the tyre lever under, and do this all the way around the circumference. If the bead is locked into the outside of the rim then it takes a lot of force to push it into the centre, UST rims have a 'hump' that you need to push the bead over. You need to apply this force directly sideways from the outside of the rim, in towards the centre. If you can do this in one spot, using your thumbs to push directly sideways then the bead will 'unlock' and you can push it around the rim more easily.
I once used a bench vice to get sufficient force to do this, but it was a last resort! risk of damage to the rim and tyre.