If I understand your question correctly, you're asking how to communicate a discount message apart from a specific product listing. So ...
Consider all your options
There are a few more solutions (possibly more common) that you've left off your list:
Save 10% and up
Save up to 70%
Up to 70% off
Keep it simple
Conventional wisdom is to first evaluate how to keep the message (essentially a call to action in this case) as concise as possible.
What is the most succinct way to communicate the offer? Of your two options, 'or more' takes that prize, primarily due to the visual complexity of too many numbers and percent signs in the alternative.
Also consider your promotional graphics. Does one format work better in the approved style than the other? This shouldn't be the driver (graphics should be altered to serve the purpose), but it's worth considering.
Remember the psychological factor
Clear and concise are nice from a usability perspective, but this is e-comm — sometimes the business comes first. Take these two options for example:
Save 10% and up
Save up to 30%
Any marketer with more than an hour of experience will bet their paycheck on the second option. It will generate more engagement. And as long as the products on the other side of that offer are desirable, it will generate more sales.
Users are drawn in by big percentage savings. 10% is a bare minimum to even consider it an offer. It's not particularly attractive. 30% is a meaningful savings.
Building on the psychological aspect of marketing, you should also consider the trigger value of the words/characters used.
There are two key triggers in the examples listed here:
%. But you may find other triggers work just as well or better, which brings me to my next point ...
Never stop testing
I say this a lot. Every audience is unique in some nuanced way. We're talking here about minor adjustments to the wording. Your audience may not respond the same way as the groups I've tested.