say I wanted to connect an existing normal push button to a IO link
master, is it possible to cut the plug of the IO link cable and
connect the button with the 3 required cores
No. You would need to get an IO-link digital interface device and connect your push button to the interface. The interface would then communicate with the PLC over an IO-Link cable.
An IO-Link system is a form of point-to-point computer network connection. It runs a specific computer network protocol over the IO-Link cable between an IO-Link master and an IO-Link device, which could be a sensor (input) or actuator (output). The master and the devices need to have some built-in computing ability in order to implement the IO-Link protocol.
If you have an intelligent sensor (i.e. one with a built-in microcontroller) it can implement the IO-Link protocol itself and be plugged in directly to an IO-Link cable. Here's a random example of a pressure sensor with an IO-Link interface.
However a normal push button doesn't have a microcontroller, it can't implement the IO-Link protocol itself and therefore it can't be plugged in directly to an IO-Link cable. Instead you need to use an IO-Link sensor device as an intermediate device between your pushbutton and the IO-Link cable. You'll need an IO-Link sensor with a digital input. (In this context "digital" means a single line carrying ON or OFF information.) You'll need to wire your pushbutton to a digital input on a sensor. The sensor will read the state of the pushbutton and send the state over the IO-Link cable to the IO-Link master and then on to the PLC. (IO-Link digital input connectors also seem to provide 24VDC and ground connections so you can power your pushbutton circuit.)
While I suspect the idea of standardising IO-Link is that any manufacturers' products can be used, as you do have a Siemens PLC Siemens also make an IO-Link digital sensor, the K20. (If you click on the booklet icon to the left of the 3RK5010-0BA10-0AA0 model number a browsable list of other IO-Link devices should appear, if not already visible.)
This may seem a roundabout way of getting pushbutton input into a PLC but you specifically asked about IO-Link. An alternative is that your PLC may have digital inputs to which a pushbutton could be wired directly.
Siemens themselves or your usual PLC supplier should be able to provide you with technical help on how to use these products. A search engine should find a selection of documents and videos to let you learn more about IO-Link.