Hey, I’m still learning SMS myself, but I believe suppressing only applies to email.   The SMS consent seems to be done manually or by the subscriber texting STOP.

To ensure your suppressed subscribers don’t get SMS as well, you can create segments and filters that include SMS consent AND email is not suppressed.  So, something like this:

I’d be curious to see if that can be done automatically though (keep the data clean!)

Hey @DarleenW 

Thank you so much for asking the Klaviyo Community about unsubscribe and suppressed profile!

When it comes to your customers subscribing to your marketing there is a difference between unsubscribing and suppressing the profile. You can customize a list’s unsubscribe page  to give your customers personalized content and allow them to unsubscribe from email only in your case. @Mailbox Manny is right, to unsubscribe from SMS within the US your customers can just text your opt-out language to your SMS number to unsubscribe. Also, check out these other Community Post about Active and Suppressed profiles:

Thank you for being a part of the Klaviyo Community!

ahh no I tested and when suppress a profile it only suppressed email 

the SMS is still active and profile still exists. 

in documentation ot clearly states this