Suddenly it's announced that my train won't go to my destination, is my Sparpreis ticket valid?

TL;DR: Your ticket is still valid and you can take any connection to your destination (and it is not relevant if you booked a SuperSparpreis, Sparpreis or Flexpreis ticket) if your train/connection is expected to be delayed by at least 20 minutes at your destination or is cancelled at all. For more information have a look at Overview of the main passengers' rights regulations

You don't need to buy a new ticket but can simply take the next train which goes to your destination. You can look up connections at bahn.de or ask the staff on you current train. Usually they are happy to help you as much as they can.

However your included reservation in the first class ticket will, of course, not be transferred automatically to a next train. You can ask the staff in the DB Reisezentrum at your interchange station to transfer your reservation and sometimes it is also possible to do this by your own in the DB app if you have a registered account. The alternative is to take the next train and simply look for a not reserved seat.

In case you missed the last regular connection of the day to your destination you are entitled for a alternative mean of transport (e.g. a cab) or a hotel room for an overnight stay. For this always ask the staff in the DB Information first, they will figure this out for you.

Besides that, if you reach your destination with a delay of more than 60/120 minutes you can get 25/50 percent of your ticket costs back by filling out the passengers' right claim form

The railways in Germany are very good in offering alternative transport if the train you have planned to use can not be used for whatever reason.
First thing to do, ask any person sitting near you to explain, if they can. Next look for a person in an uniform. And if non is near, go to the ticket office in the station you are.

The uniformed staff or ticket window staff will tell you which train you can best use, sometimes giving you an alternative route.
You may not get a reserved seat on the alternative route, as that can not always be arranged, but in first class you can almost always find a seat or ask the train staff to help you find one.

I have had the same kind of problems several times in Germany, always got to my destination on the same day, if a little later than planned. And at no extra cost.
If your delay make you miss your last train of the day, they are supposed to help you reach your final destination that same night or put you up for a night, but you will have to ask uniformed staff or ticket office staff as soon as you have a reasonable expectation of that happening, to allow them to arrange things.