Interesting question Ramesh. There are 2 ways to do this:
You create a new website in area of your industry/service. While disclosing your association (e.g. Powered by YourOrganization), you can create content which is neutral and target competition. It's likely to take some time to get rankings but you'll have a lot of flexibility in terms of scope of coverage.
Create comparison page on your website. This is a normal practice and done by many companies especially in Tech Products space. Make sure that you are providing correct & factual information and give disclaimer in terms of respecting trademarks.
On the other hand, you can surely target competitor keywords using SEM/PPC in Search campaigns. If you want to target the email recipients of your competitor, you can use Gmail Ad campaigns. Btw, Twitter Ads also allow targeting followers of an account.
Does this help? Let me know if can be of any help regarding targeting competition.