I am able to double/possibly triple my mortgage repayments due to an recent inheritance I have come into. Would it be advisable to reduce the amount of time I have taken the loan for, or to pay the extra directly off the principal of the loan? Thank-you

First be sure you don't owe any taxes on it, including state.
Second, you can't shorten the term on your own - only the lender can, and they won't unless it's rewritten, with all the attending fees.
Third, it depends on your financial situation in general and on the current rate of your loan, and whether it's fixed or adjustable. If most of it is still interest, and having the deduction is a big help offsetting your income at tax time, don't do it; invest the money instead. But even that depends on your ability to chose investments that are fairly safe but yielding higher rates than your loan, very possible even now, not CDs paying 1.5%.
If the deduction isn't helpful, or you are paying a higher rate than currently available, then yes, pay down the principal. If your agreement allows it, which most don't in the first 2 years.
Work out all the scenarios to your best advantage.

Why was this posted in Homework Help-Finance and Accounting?

Is this is a residential mortgage? Or a problem assigned by your teacher?

As noted you can't reduce the term of the loan, but you CAN pay it off sooner, saving you interests costs by paying more. Anything you pay over the required payment will go towards reducing the principal. By doing so you reduce the amount of interest owed for the next payment (look up amortization).