Well, I guess you came here because Limesurvey might rank high for "survey tool", because there is no thing like a "if this then that survey tool".
But lets go to what you are asking for. You are describing two different things here:
1. Screen out (if this answer then end survey)
2. Filtering (if this answer then don't show this question)
Both things can be done in Limesurvey.
1. Screen outs are not impleted as a own function. You will need to use quota, more specifically a zero quota. This will close the survey once the number of answers you put into the quota is reached. With a zero quota this means if someone gives this answer, the survey is automatically finished. You can even give them a specific message.
2. This are so called conditions. You can do it via the interface. But since a few versions we have something that is called Expression Manager, which allows to create this conditions via a little code and it is a lot quicker. You just write into the relevance equation things like this:
Q1 == 2
This would mean that the question is only shown if in question Q1 the code 2 is checked. Pretty easy and really quick. Better than clicking through all the GUI.