Yes its possible actually. If I understand your question your requirement is to prevent users from creating new tasks and event from the task page. You can go to the desired profile ->System Permissions->Disable Edit Events check box(or Disable Edit Tasks check box)->Save
Hope these links help you.
http://www.ceus-now.com/removing-save-new-task-save-new-event-button/
https://success.salesforce.com/answers?id=90630000000gvWnAAI
Best Regards,
BALAJI
Yes its possible actually. If I understand your question your requirement is to prevent users from creating new tasks and event from the task page.
You can go to the desired profile ->System Permissions->Disable Edit Events check box(or Disable Edit Tasks check box)->Save
Thanks
Rupal Kumar
http://mirketa.com
Whatever you say I already done but issue not resolved.
There is no standard way to hide save and new task button on Edit page. As of my knowledge, one possible way to accomplish is Visualforce.