Since you are not sequencing single cells, you cannot easily "remove" the normal cells. But you probably did not mean that literally anyways.
By comparing tumor and normal, you can detect alterations that are present only in tumor using somatic variant callers (GATK, MuTect, Strelka, ...).
Quantifying the normal contamination in the tumor sample is a bit more complicated, but there are a lot of other tools published recently (e.g. FACETS, Sequenza, ...) for paired whole-exome sequencing.
We recently published the Bioconductor package PureCN that in addition adjusts read counts of somatic and germline variants in a VCF for normal contamination and allele-specific copy number (paired or unpaired whole-exome sequencing).
You can finally use tools like PyClone or SciClone to "cluster" the tumor cells into different clones.