Mine looks like this.
They don't "pull apart" it is threaded!
You could use the choke wrench on the muzzle end, securing the muzzle brake portion in a protected vise.
I would think the best approach would be to secure the muzzle end in a protected vise and use a cross bar thru the muzzle brake apertures to turn the part, less likely to mar the parts that way.
Use a good penetrating oil first! e.g. Kano Kroil and let is soak for hours, then apply methods.