Is there a Data Structure like Binary Decision Diagrams for Non-Binary Functions Binary Decision Diagrams (BDD) take a set of binary variables $x_1, x_2,..., x_n$ as input.
Is there a data structure similar to BDDs where each variable takes more than two values? Each variable's values should be independent of every other variable. For example, $x_i$ could be assigned the three values $\{0,1,2\}$ and $x_j$ could be assigned the four values $\{0,1,2,3\}$, where $i \ne j$.
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.