Here's some information to get you started ...
Let's assume your Sawtooth survey is structured as follows ...
Q1-Q10 (your Sawtooth survey - part 1)
Skip to other survey
Q11-Q15 (your Sawtooth survey - part 2)
When your Sawtooth survey has reached the point where it's time to skip to the other survey (Q10 in the above example), setup a termination question at this point. Do not file away the survey as a complete or disqualify as you want it left as incomplete to enable the survey to continue after the other survey has been dealt with. So don't tick the terminate respondent box in the terminate question. Tick the link to a questionnaire or website and enter the link.
You need to include an ID or password in the link to the other survey. See example below ...
You will need to pass the "id" from your Sawtooth survey to the other survey and back again. This will enable Sawtooth to know which survey is being continued (via the "id").
When the other survey has been completed, you need to skip back to Q11 (as per my example above) to recommence your Sawtooth survey at the correct suspension point.
It will look something like this example ...
Note the "&sys_skipto=Q11" at the end of the survey link which enables you to skip back to your Sawtooth survey from the other survey. You just need to identify the question name in the returning survey link.