GATK workflow for Cancer
This post goes over what MuTec requires as input. mark duplicates and indel realignment will probably have to be done on bam file to use it as input. BQSR is optional and does not change the quality too much. HaplotypeCaller is used for germline not somatic variant calling.

If you have followup bioinformatics questions, you might be able to find answers more quickly on biostars or GATK forums