Hi David,

Greetings to you!

You can use force:refreshView to request a page refresh. Try like this:
 

clientMethod : function(component,event,helper) {
        var action = component.get("c.serverMethod");   //calling server-side method
        action.setParams({
        "serverParameter":clientParameter
    });
        action.setCallback(this, function(response){
            var state = response.getState();
            if(state === 'SUCCESS'){
                $A.get('e.force:refreshView').fire();
            }
            ...
            ...
            ...
        )};
        $A.enqueueAction(action);
},

/*page refresh after data save*/
    
    isRefreshed: function(component, event, helper) {
        location.reload();
    },

And don't forget to add below handler in your component:

<aura:handler event="force:refreshView" action="{!c.isRefreshed}" />

Or you can call init method in handler action: <aura:handler event="force:refreshView" action="{!c.doInit}" />

Please try the below code, I have tested in my org and it is working fine. Kindly modify the code as per your requirement.

Apex:

public class UpdateDataTable_TaskSvrController {
    
    @AuraEnabled
    public static List<Account> details(){
        List<Account> lst = [SELECT Name, Phone, Rating, NumberOfEmployees FROM Account LIMIT 10];
        return lst;
    }

    @AuraEnabled
    public static List<Account> updateDetails(List<Account> lstForm) {
        update lstForm;
        return lstForm;
    }
}

Component:

<aura:component controller="UpdateDataTable_TaskSvrController"
                implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction" access="global" >
	
    <aura:attribute name="PageHeading" type="String" default="Update Using Data Table"/>
    <aura:attribute name="mydata" type="Account"/>
    <aura:attribute name="mycolumns" type="List"/>
    
    <aura:handler name="init" value="{!this}" action="{!c.doInit}" />
    <aura:handler event="force:refreshView" action="{!c.doInit}" />
    
    <div class="slds-m-top--xx-large">
    	<div class="slds-page-header">
    		<div class="slds-align--absolute-center">
        		<div class="slds-text-heading--large">       
    				{!v.PageHeading}
                </div>
        	</div>
    	</div>
    </div>
    <br/> <br/>
    
    <div id="dt">
        <lightning:datatable aura:id="iliDataTable"
                             data="{! v.mydata }"  
                             columns="{! v.mycolumns }" 
                             keyField="Id" 
                             hideCheckboxColumn="false" 
                             onsave="{!c.saveTable}" />
    </div>
</aura:component>

Controller:

({
    doInit : function(component, event, helper) {
        component.set('v.mycolumns', [
            {label: 'Account Name', fieldName: 'Name', type: 'text', editable: true, initialWidth: 750},
            {label: 'Phone', fieldName: 'Phone', type: 'phone', editable: true},
            {label: 'Rating', fieldName: 'Rating', type: 'text', editable: true},
            {label: 'Number Of Employees', fieldName: 'NumberOfEmployees', type: 'number', editable: true}
        ]);
        
        var action = component.get("c.details");
        action.setCallback(this, function(response) {
            var state = response.getState();
            
            if (state === "SUCCESS") {
                var res = response.getReturnValue();
                component.set("v.mydata", res);
            }
            else if (state === "ERROR") {
                var errors = response.getError();
                if (errors) {
                    if (errors[0] && errors[0].message) {
                        console.log("Error message: " + 
                                 errors[0].message);
                    }
                } 
                else {
                    console.log(response.getReturnValue());
                }
            }
        });
        $A.enqueueAction(action);
    },
    
    saveTable : function(component, event, helper){     
        //var data = component.get("v.mydata");
        var draftValues = event.getParam('draftValues');
        var action = component.get("c.updateDetails");
        action.setParams({lstForm  : draftValues});
        action.setCallback(this, function(response) {
            var state = response.getState();
            
            if (state === "SUCCESS") {
                var res = response.getReturnValue();
                $A.get('e.force:refreshView').fire();
                alert('Updated Successfully...');
            }
            else if (state === "ERROR") {
                var errors = response.getError();
                if (errors) {
                    if (errors[0] && errors[0].message) {
                        console.log("Error message: " + 
                                    errors[0].message);
                    }
                } 
                else {
                    console.log(response.getReturnValue());
                }
            }
        });
        $A.enqueueAction(action);
    }
})

CSS:

.THIS {

}

.THIS.slds-size--3-of-8 {
    
    margin-left: 430px;
}

I hope it helps you.

Kindly let me know if it helps you and close your query by marking it as solved so that it can help others in the future. It will help to keep this community clean.

Thanks and Regards,
Khan Anas