If they do sometimes still throw a branch of the true, original color, then the
scion (top of the graft) is not dead. Find the graft union -- a thickened,
fist-like knot low on the stem. Cut off all branches originating below that
lump, but keep all branches coming out of the lump itself or above it. With
many varieties, the leaves and thorns will also be somewhat different on the
scion vs. the rootstock.