This is usually a bad practice. catch(Exception e) (sometimes called Pokemon Exception Handling for when you gotta catch 'em all) catches every single exception. Such exception handling is rarely useful because:
- It catches runtime exception too.
- You lose information about the type of exception that was thrown.
- You cannot react to or handle specific exceptions.
Your method signature now is public void whatever() throws Exception, which is rarely useful. Now everything further up the chain has no idea what kind of exception you have thrown; they will have to do instanceof checks which defeats the purpose of catching specific-exceptions entirely.
As far as your second exception is concerned, throw e; throws the same exception object. If you wanted to wrap the exception, you can create a new one, which means you would do something like throw new MyCustomException(e);. You would also need to change your method signature.
If there is nothing further up the chain, I guess this isn't as bad (still isn't great, though). It looks like a method that is trying to log all exceptions that are thrown. However, again, there are better ways of doing this.