Your dog may be destroying your mini blinds for a couple of reasons. Most likely, it just enjoys chewing on them and has not been taught an appropriate outlet for chewing. Almost as likely is that your dog is barking at passersby and redirecting its excitement on your blinds. Finally, when dogs are exhibiting separation anxiety, they may destroy things, particularly doors, windows and blinds. While this is unlikely, it must be explored if traditional training methods aren't working.
Teach Your Dog Not to Destroy Mini Blinds
Try to determine why your dog is exhibiting this behavior. Does it bark at the window when you are home? If so, it is probably redirecting its energy on the blinds. Does it get nervous as you prepare to leave? This may be separation anxiety. If not, your dog is probably just chewing on the mini blinds because it doesn't know what else to chew on.
Prevent your dog access to your blinds while you are gone. Regardless of the reason, your dog shouldn't be able to practice this behavior unless you are there to supervise and teach a new behavior.
Teach your dog a leave it command. Get a handful of treats. Allow your dog to have one and say "take it." Repeat a couple of times. Close your fist and say "leave it." Be patient while your dog paws, nibbles and barks at you. Ignore all undesirable behavior. Keep your fist right by your pup's nose. When he looks up at you, praise and allow him to take it. Repeat this until you can hold a treat in your open fist without your dog reaching for it.
Teach leave it on the ground by placing a treat on the ground, placing your foot over it and saying "leave it." The only difference between this and Step 3 is that you don't want to let your dog have the treat on the ground. Reward from your hand. Practice this until your dog can leave a treat on the ground without you putting your foot over it. Then begin practicing with many objects, including the mini blinds. Each time your dog goes near the mini blinds, give the command. If it listens, reward it by redirecting it to an appropriate chew toy.
Teach your dog to go to its bed rather than bark at the blinds if this is the problem. Keep it on leash and send it to its bed each time it barks. Reward it for staying on its bed. If your dog can't listen, take it to a time-out area, such as a crate or bathroom. Allow it back once it has calmed down. Practice this until your dog can automatically run to its bed rather than bark. Give lots of rewards for a job well done.