You are the spitting image of your father. The whole phrase is "spit and image" and means you are made from and look like someone. This phrase is recorded in a book published in 1901. The use of the phrase "dead spit" to mean "dead ringer" is found in the 19th century.
An alternate theory is that the original phrase is "spirit and image" and means you are alike body and soul. Then there is the theory that the phrase started as "splitting image" meaning you are as identical as a plank of wood splint in two. These theories are certainly more sourced in distaste for expectorate references than actual usages.