I want to check whether some specific miRNAs have putative binding sites in genes specifically participating in apoptosis process. Can anyone please suggest me some computational tools for the same?
as you know miRNAs bind to transcripts and not to their corresponding genes but, you know, we can use gene specific annotations to actually define transcrpts biological functions. This is what bioinformatic tools for miRNAs functional genomics do using information on miRNA targeting (that may result from predictions or experimental procedures). On the functional genomics part of your question I can suggest you miRó: the mir-ontology database.
You can explore the database performing a search based on the term apoptosis and then check for details of miRNA/mRNA interaction, including the putative binding site.