Looking for a way to have a warp example image on a stock mug photo/image but able to change out the example image using replace content. Hoping not to warp each example image but a preset template.
Use smart objects. You create the smart object and apply the warp to the smart object. You can then change the contents of the smart object without needing to apply the warp again.
Note: I haven't spent much time getting the warp correct, this is just a quick example, so it doesn't look great.
Create a shape roughly the size you want the placed image to be. As you will be swapping the content we need a base size to place the image on. This depends on how much of the mug will be covered by the images. If this will vary, make the shape as big as the biggest area that will be covered. Possibly the entire surface of the mug.
Create a smart object from the shape you created. You can do this by going to the menu 'Layer > Smart Objects > Convert to Smart Object' (make sure the shape is the selected layer). Or you can right click the Layer and select 'Convert to Smart Object'.
Warp the shape to fit the mug. (cmd+t to free transform, then right click > warp).
Double click the smart object layer. This will open the smart layer as separate document in a new tab. You can then paste your image into this layer and position how you like. Position the image so only the first half of the image is visible.
Saving the smart object will auto update the object in the main document.
For the other side you can then simply flip the mug image and update the smart object to show the other half of the image. Or repeat the whole process for the other side if you need to use another mug image.
You can save this as a template and for every new image you need to mock up you simply paste the image in to the smart object.
To get realistic picture-like results, have a look at the Photoshop 3D tools. You can use a basic cylinder kind of 3D, adjust it to the cup size and then add it over a layer that has your cup image. You can find tutorials and even basic shapes online.
The benefit is that you can easily add shadows and lightning effects. Even imperfections that make the print look more realistic. The perspective and wrapping are perfect, and once your template is done, it's very fast to update it with another image; just a double-click, copy/paste and save! You can use any size of image, as long they fit within the frame. The final result is very close to the real object or a picture of it. If that's what you want, then explore this option.
The only bad sides of this is you need a computer that can handle some 3D, you might need to learn some basic 3D and there's also a certain investment in time for rendering your images when you're done. But the result will be as good as a picture taken in a photography studio.
Smart object can work too but the final result will match your own skills in wrapping the image in a realistic way! It's not always easy to distort the image around a curved shape and you'll need to add the shadows/highlight manually (if you want a very realistic result.)