Neither X-Plore, or any other file manager, will be able to move an app. Nor would Tasker. Even if you had access to the place where the app is stored (which requires root) if you simply moved it it would stop working because the phone wouldn't be able to find it. What you would need to do is move the relevant folders and put links in their place to redirect calls to them to their new locations (this is basically what the operating system does when it moves an app).
As said above, not all apps support that (it's up to the developer, and with more phones having larger internal storage and maybe no SD card there's less incentive for them to do so). So if this app doesn't support it, and your phone doesn't support formatting the card as internal, you really only have 3 options:
1) root the phone, partition the SD card, then use something like Link2sd to move apps.
2) without root you could use ADB to set SD as your default storage. This makes more apps moveable (though not all, so no promises). The command is (from memory) something like "adb shell pm set-install-location 2".
3) Live with it.
You don't say how much of the 70MB is the app and how much its data. The system move to SD (default or after using the ADB command) only moves the APK and any shared object library, not the dalvik/ART part of the installed app and not the internal data. So you should expect to save a part of whatever part of that 70MB is app rather than data. You can choose to move more with the root method, but it's more work.