I would like to see how the image will be displayed on the monitor with lower color gamut.
Am I able to mimic this using Photoshop?
Yes. This is called colour proofing.
First, make sure you have colour management enabled, that is, the image has a colur profile assigned (check in Edit −> Assign Profile), and generally the colour seetings are set as required (Edit −> Color Settings and the display profile in your OS). Thus, you ensure that the image is correctly displayed on your monitor as is.
Then, go to View −> Proof Setup and select Custom. (Don't just select sRGB from the menu list). There, select the Device to Simulate to your target narrower profile (e.g. sRGB for a typical consumer monitor).
Now you need to decide what exactly do you want to simulate. There are two major possibilities:
The user (of that consumer monitor) doesn't bother with colour management (which is necessary even for correct image viewing), AND you send them your wider-gamut image (even if with a correct profile attached). The colours will invariably be distorted (mostly desaturated, even if your image entirely fits within the narrow gamut), and you want to simulate this scenario. Select Preserve RGB Numbers.
Unfortunately, this is still a very common situation. To minimise the damage of this kind, you should convert your images to sRGB for such users (which means in practice: for any external use where you don't have control over the workflow).
The user does apply proper colour management when viewing images (by the virtue of the OS or specialised software), OR you want to do it for them (to some extent) by converting the image to sRGB (as advised above). In this situation you will lose the most saturated colours (if they are present in the image), but most other colours will be unaffected. To simulate this scenario, uncheck Preserve RGB Numbers and select the desired conversion method. You should select 'Perceptual' or 'Relative colorimetric' (this is what most users have); the difference between them is small.
Very possibly, you won't see any changes in the image. This is good: it means the image doesn't have any colours that don't fit to the narrower gamut. To be extra sure, select View −> Gamut Warning (after closing the 'Customize Proof' window): in this mode all out-of-gamut colours are filled with grey, making them visible. Note that this mode is not applicable to the first scenario and so won't be selectable: all colours fit there by definition, but all get distorted.
After setting up the proof mode, toggle View −> Proof Colors (Ctrl+Y) several times to see if there is a visual difference.
You can keep editing your image with proofing enabled. However, keep in mind that you are in an emulated mode. If you just save and distribute your image, you may inadvertently end up in scenario 1.