Is it possible to pay with a Swiss Francs bill that is cut into pieces in a Swiss store such as Migros or Coop?
I guess it depends on jurisdiction, but in some (all?) European countries you can present a stitched banknote and have it accepted as a legal tender by a merchant. One requirement is that the Frankenstein banknote is almost whole, i.e. only small parts of it are missing (otherwise one could try to use two halves of the same banknote in different places!). I assume some the security elements of the banknote should also be present for it to be accepted - for example, in some countries there is a hologram strip on one side of the banknote which should not be damaged.
If it's in two or three large pieces, I'd repair it and try to use it for payment -- just don't conceal it among other banknotes to hide its state!
If it's too badly damaged, I'd go directly to the bank and try to exchange it there.
In case of the Swiss Franc, this is regulated in the Federal Curreny and Means of Payment Code (Bundesgesetz über die Währung und die Zahlungsmittel / Loi fédérale sur l’unité monétaire et les moyens de paiement).
Article 8 states that a damaged bank note is replaced by the Swiss National Bank if the serial number is recognisable and at least half of the bank note is provided.
Similar regulations are in effect in at least the Euro zone and I assume most other European countries. Some countries operate with a disclaimer that deliberately damaged notes are not replaced.