Hi,

You can't achieve this using standared controller.

You need to use controller extension or Controller for this.

Modify your VF code like below  and let's say page name is "saveandnew"

<apex:page standardController="Work_Performed__c" extensions="saveandnewclass">
<apex:form >
        <apex:pageBlock title="Work performed">
            <apex:pageBlockButtons >
                <apex:commandButton action="{!saveandnew}" value="Save"/>
                 <apex:commandButton action="{!cancel}" value="Cancel"/>
            </apex:pageBlockButtons>
            <apex:pageBlockSection title="Work Performed" columns="2" collapsible="true" dir="LTR" id="My">
                <apex:inputField value="{!Work_Performed__c.Note__c}"/>
                <apex:inputField rendered="false" value="{!Work_Performed__c.Case_Number__c}"/>
               
            </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>

 Create new apex class,the controller code will be

public with sharing class saveandnewclass {

     Work_Performed__c wpc;  
    ApexPages.StandardController sController;  
    
    public saveandnewclass(ApexPages.StandardController controller) 
    {
        sController = controller;
        wpc = (Work_Performed__c)controller.getRecord();
    }

public PageReference saveAndNew() {
        
        // Custom Save code here...
        
         sController.save();
         PageReference pageRef = new PageReference('/apex/saveandnew');
         pageRef.setredirect(true);
        return pageRef ;
    }


}

 Try this Code.

your problem will be solved and you will be redirected to same page after saving the record,i.e save and new Functionality.