You can find the branch point using git merge-base. Consider master the mainline and dev the branch whose history you are interested in. To find the point at which dev was branched from master, run:
git merge-base --fork-point master dev
We can now diff dev against this basis:
git diff $(git merge-base --fork-point master dev)..dev
If dev is the current branch this simplifies to:
git diff $(git merge-base --fork-point master)
For more information see the git-merge-base documentation.