I have a list of mutations as VCF1.vcf, and another list of mutations as VCF2.vcf.

I need to exclude mutations in VCF1.vcf that are appearing in VCF2,vcf, and save the result as a new vcf file.

What could be the most elegant way of doing this?

This could be a job for VariantAnnotation::filterVcf(), including the prefilter= argument; see the filterVcf vignette available from the VariantAnnotation landing page https://bioconductor.org/packages/VariantAnnotation, as well as help page. It's difficult to provide additional help without knowing what 'appearing in' means in a computational  sense.