Is there a Data Structure like Binary Decision Diagrams for Non-Binary Functions
Yup.  A BDD is just an acyclic finite-state automaton (DFA) that accepts a language $L \subseteq \{0,1\}^n$.  It represents the function $f(x)= 1$ if $x \in L$ or $f(x)=0$ if $x \notin L$.

You can generalize this to allow an acyclic finite-state automaton over a language over a different alphabet, or indeed, a language $L \subseteq \Sigma_1 \times \cdots \times \Sigma_n$ where $\Sigma_i$ is the set of valid values for $x_i$.  Everything carries over.