Get your slimy, webbed phalanges off ma boots!
If I choose the purple die and select a die face that is the same colour as my titan, does the Life Point gain negate the Life Point loss from using the purple die?
You only gain a life point when you choose a die face with the same color as your titan. When you choose the purple die face, you take the action of another die face, say yellow (but that is not the same as choosing the yellow die face).
So no titan ever gains a life point when choosing the purple die face. All titans, with the exception of Chtooloo, lose a life point when choosing the purple die face.