The safest way to reach IIT Mandi from Chandigarh is to take a flight to the nearest airport, which is Bhuntar Airport in Kullu. From there, you can hail a taxi or bus to IIT Mandi.
Another way to reach IIT Mandi is to take a train to Joginder Nagar Railway Station, and then take a bus or taxi to IIT Mandi.
You can only hail a bus or a cab from Mandi. Volvo buses are very comfortable and safe. You can book tickets for these buses from the HRTC ticketing website. The buses are run by experienced drivers who are quite familiar with the route.
Additionally, it's always a good idea to plan your trip in advance, so you can make sure to have all the necessary information, such as transportation schedules and safety precautions.