Have you considered eQTL tools / database for this task ?

If your mutation is already recorded in dbSNP you could get eQTL/ expression quantitative trait variants (eQTV) data for variants of interest (See eqtl questions discussed here, most of the questions are genotype/GWAS centric, but still will help you to understand major set of tools/databases). If your mutation is a novel SNV, you need to do experimental/prediction studies to figure out the effect of mutation on gene expression.

Following papers will be useful:

• Rare and Common Regulatory Variation in Population-Scale Sequenced Human Genomes

• The study of eQTL variations by RNA-seq: from SNPs to phenotypes.

• Transcriptome genetics using second generation sequencing in a Caucasian population.

You need to search for "quantitative trait association testing" and will find most likely find PLINK. You could make a quantitative trait from the expression value, e.g. log RPKM. This could work in principle, if you had enough cases. However, most likely you will have only a handful of cases because you mentioned mutations, and the mutation alleles can be very rare, such that nothing significant will come up. If you however confused mutation with SNP and have a lot of cases, things might look different.