I have done three differnt methods,two of which have already been suggested .I have lapped a normal bevel and a reversed bevel, I have made the intersection look like a v-groove, and I have used decrotive geometric pieces of matting ( matching colors or contrasting colors) to cover the seam .
The most difficult is the opposeing bevel thing ,since it is all but impoosible to not see the seam,(especially by the one doing the matting ot if you tell someone else. When you know it is there your eye goes almost automatically straight to it.
I have spliced segments to form v-grooves in a decrotive pattern( e.g- i ahve added small segments on the bias to form musical scale lines and then cut out notes on these lines to appear like sheet music for a N.O. Jazz and Heritage poster .I have also cut small tiangle shaped segments that covered the seem and then matched them on the non-spliced sides.( this was done for Lion fish drawing that was done on a full sheet of Illustration board).I have also matched the pattern of an African Rafia Cloth and used the segments of the pattern to extend the mat on all sides since the cloth was 3.5 feet wide by 7 feet long.
In my humble opinion the key is to not try to hide the seam but to icorporat eit into the design. Or as My old friend Bill Parie would say "Paint It Red' when you try to hide it it looks like an error ,no matter how good of a job you 've done.
I have concealed a mis-cut on a very involed oriental mat design by bringing the two opposeing bevels together and putting a small dab of glue on a strip of release paper and draged it through the splice ,then covering the splice with another piece of release paper and brunishing the seam and then weighting it until dried.I can still find it every time but it has hung on the wall for over 10 years and no one has seen it yet.( in fact if you look at my Gallery of design pictures and you see the oriental design that is itand i'll bet you didn't see the splice)LOL
BUDDY