If the compiler was written in Java, then you execute it the same way you execute any Java program. Compile it with bin/javac from .java to .class Then you execute that .class with bin/java. Your program then produces the llvm-ir code, which you then can use to build a binary or execute it directly with LLVMs program lli.

I don't see what you would need GraalVM for. Also I don't see why this question is tagged with "compiler construction", because nothing in it is specific to compiler construction.