You have numerous options to reach IIT Mandi from Hyderabad. It will be a 12-hour journey from Hyderabad.
The best way is to catch a flight to New Delhi, and after that, you can travel by bus from ISBT Kashmere Gate to Mandi. From there, you can easily reach the campus.
You can opt for HRTC, which has more experienced drivers and is ideal for long, safe journeys at a low cost.
The next easy alternative is to take a train from Hyderabad to New Delhi, then you can either catch a flight or bus according to your convenience to reach Chandigarh and finally, you can reach Mandi by bus. From Mandi bus stop, there is a regular institute bus or HRTC that will take you to the IIT Mandi campus.