Roku app won't connect to my TV whikst using mobile data

The Roku app will only connect to a Roku TV/Player if both are on the same private network. If you're using mobile data on your phone, then you are not connected to your personal network. This is a security feature. You cannot use the app to control a Roku unless both devices are on the same network and that network is using a Private IP address configuration. In most cases, a home network IP address should begin with 192.168, with the last two octets having a zero or one on the third octet and a number between 2 and 254 in the last octet. Note that in a home network, the first three octets must always be the same number, with only the last octet being different for every connected device. There are exceptions to this, but it's highly unlikely that a home network would used something different.

Also, if you're using a shared WiFi, such as a dorm, hotel, or some apartment complexes, those will have security enabled that will block your phone with the app from seeing your Roku, so the app will never work on such networks.