You cannot throw multiple exceptions at the same time in Java, but you can throw multiple different exceptions at different times.
Here's how you do it:
public void myMethod() throws IOException, SQLException {
  // …
  if (/* some condition */) {
    throw new IOException("first exception");
  }
  // …
  if (/* another condition */){
    throw new SQLException("second exception");
  }
  // …
}
