There are differences in meaning or focus. Let us start with the simple statement:
Ich schreibe das Wort aus.
→ I am writing the word out.
If you want to express, for whom you do it, you can use a personal pronoun, such as mir:
Ich schreibe mir das Wort aus.
→ I am writing the word out for me.
The english reflexive pronoun myself is typically translated to the german demonstrative pronouns selbst or selber. It is used to focus on the fact that you yourself did something, rather than someone else:
Ich schreibe das Wort selber aus.
→ I am writing the word out myself.
As an aside, note @Hagen von Eitzen's comment, where he asks if you really want to express that the word is written out completely, opposed to incompletely for whatever reason. Possibly, you rather wanted to say something like this?:
Ich schreibe das Wort auf.
→ I am writing the word down.