I have a button like the above 1st image. If I am pressing that button it will display the Stacked Action items like in picture 2. By pressing the any of the stacked Action button it will go to the next page but its in a web application and I want the same design in mobile, so what is best approach or design for mobile?
Unfortunately I don't know the exact purpose of the button. But for this kind of options the dropdown seems to be unsuitable. Perhaps use a solution like
[Stretch for X min] [-5min or up arrow] [+5min or down arrow] or [skip]
X is a variable and can be changed by the +/- buttons. It is easy to use and contains your 5 min step size. Additionally it is good to use at mobile devices and space efficent.
I think this solution implements your options properly and you can preset the most common duration for your users.