Rent or buy a grinder and get a diamond blade. Use that to cut and dig out old mortar. This is a very handy item combo to own for lots of house repairs.

up new mortar and pushing it into the joint is not to difficult. Need to get the proper tools. It's a doable DIY. Cover everything under it and have water a rag and brush to wipe brick before mortar sets (the face of the brick will get some on it, and if left to dry it's a big pain to remove.)