The base form is 멈춰서다 (to stop (in one's track)).
It is a compound verb comprising 멈추다(stop) and 서다(come to a stop) but it behaves just like any other verb.
1. 멈춰서도 = 멈춰서(다) + -도 (verb ending expressing "even if (you do the action)") => even if I stop (not a full sentence).
2. 멈춰섰다 = 멈춰서(다) + -(아/어)ㅆ다 (sentence ending form in the past tense) => (I) stopped (full sentence).
There is a whole bunch of verb forms (conjugations) besides '-도', and another set of sentence endings. Knowing these forms is probably the most important part of learning Korean.