How can I clear a blockage caused by the previous owner flushing grout down the toilet?
This is really a comment but too long - 

I am not sure of your exact situation but normally if something like this happens you call your real estate agent, police, and bank.  You need to file a police report, your real estate agent needs to get a hold of seller's agent (who is ultimately responsible in most states), and you need to talk to bank about freezing any money if you can.  It might be too late for this but I don't know.  But whatever it is the previous home owner (if can be proven) has committed a criminal act.  Not taking action right away hurts your case.

There is no magic to get rid of stuff like grout in pipes.  First any serious chemical I might suggest may damage the pipes.  Second I am not even sure it is grout in your pipes - it could be various types of cement or thinset too...  Then I am not sure to what extent the material got in.   This could go all the way to the street which may cost a lot of money - I have seen a similar scenario run home owner 15K done cheaply.  

Also most insurance  companies don't cover criminal acts that aren't reported.  But the issue you have here is that this probably happened before you officially had insurance (that is why I mentioned getting agents involved).  If you have some sort of new home owner's insurance that might cover it but they will basically be going after the previous owner for you.  

Right now you need to file a report, take a TON of pictures and video and have a plumber come out.  You can't start hacking everything up or you are making it worse.  The plumber will be able to scope the line to see what the extent of damage there is ($200-300 tops).   The last thing you want to do is repair something incorrectly or cause more damage (overflow) and have it blamed on something you have done.