Is it possible to repair Dugast tires without cutting them off and repairing the inner tube only. Something like these TUFO sealant?

There is our national championship next weekend and I dont know if I can get new one in time.

it wil work probably, but if you use sealant, You'll probably ruin the casing, making it impossible to do the former repair later.

I wouldn't put that stuff in a nice tubular like the dugast, IMO it's more usefull in a road tubular to prevent you from having flats in the first place and to get you home when you do flat without having to take the tub off first. With the super low tire pressures used in cx I don't think it will work as well.
You're probably better off just taking the tubular off the rim and repairing it the old way, that way you are sure that the result will last. Would be a bad thing to mess up your championchips because you'r tire didn't hold wouldn't it?
The dugast's aren't that hard to repair, they are much easier than most newer road tubulars. I would say learning to do it yourself is pretty usefull.

I still got the tire of the rim and opened it where the puncture is. Any idea how to repair the inner latex tube and get the tire closed again.

I take it you already found the leak? It's best to repair the hole with a small patch of latex tube but you can use standard patches for these as well if you don't have an old latex tube. (try and get some subtle patches that are thicker in the middle and very thin at the side, in my experience these work best).
When you have repaired the tube and everything is cured well you have to get the tube back in the casing. Depending on how much you opened the casing this can be a little tricky. I always use some talk powder to get everything in there more smooth (don't want to start a debate like on the road forum again, some there argue that the talk powder does nothing but this is how I do it ) Whatever you do don't pump up the tire to try if the patch is holding at this point! If you do the tube will probably get out of the casing and explode and you will have to replace the whole tube...
Now comes the tricky part, stiching it all back together again. Some bike shops will have special thread to do this, it's strong and sometimes wax coated. Just use something that looks like what's already there. If you opened the tire by cutting all the thread that was around the puncture you have to use new thread all the way, if you carefully unthreaded it you can use some of the original but you will still need some new to close the last little gap. If you think it's not strong enough do it twice.
Last thing is to reglue the basetape on the rest of the tubular, make sure you use strong and waterresistant glue for this as you don't want it to get loose when on the bike.
When the glue is tried you can now trie to pump up the tire to see if you repaired it correctly. I always do this before mounting it back on the rim just to make sure I didn't mess up.
When the air holds only thing to do is to reglue the tubular to the wheel and it should be as good to use again.
It isn't really hard to do but take your time to make sure you do it right (otherwise you'll be doing it twice). If you have done it a couple of time's you'll get quicker.
Good luck and let us know how it went on the nationals!