What happens to the cut-out introns from a pre-mRNA?
Yes. Ribonucleases (RNAses) break down the spliced RNA strands back into mononucleotides, and these building blocks can be reused. 

They will be broken down into nucleotide monophosphates, so they will have to be re-phosphorylated to triphosphates before they can be reused for transcription.

Here are a couple of reasonable reviews of the mechanisms: 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3177198

Note: this one also mentions that sometimes introns are not fully degraded to single nucleotides, but instead can serve as signaling molecules.

http://www.sciencedirect.com/science/article/pii/S0092867409000671