This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
since your m2() throws two Exceptions you need to handle them in m1() too.
In your case you can handle the exception in one method either m1() or m2(). If you want to handle exceptions in m1() then avoid catching them in m2(). If you want to handle the exceptions in m2() then avoid throwing.
However the above suggestions are subjective and Exception handling should be done based on your requirment.