You can use the camel query to get the list item based on your column value which will load only those list items which meet that criteria, then do the delete operation as usual way. 

**Sample Example: Using JSOM**

To filter SP.ListItem's on multiple conditions, there are no single methods that take the arguments as multiple filter fields. Instead, you'll have to resort to using a CAML query to specify the list items you want, as below.

 

    var clientContext = new SP.ClientContext( siteURL );
    spList = clientContext.get_web().get_lists().getByTitle( myListName );
    
    //Create a CAML-query with your filter conditions
    var camlQuery = new SP.CamlQuery();
    camlQuery.set_viewXml('<View><Query><Where><And><Eq><FieldRef Name=\'Age\'/>' + 
        '<Value Type=\'Number\'>30</Value></Eq>
        <Eq><FieldRef Name=\'Country\'/>' + 
        '<Value Type=\'Text\'>US</Value></Eq></And></Where></Query><RowLimit>10</RowLimit></View>');
    
    //The query will return a collection of items matching your conditions
    this.collListItem = spList.getItems(camlQuery);
    
    clientContext.load(collListItem);
    
    //Execute the query
    clientContext.executeQueryAsync(function () {
    
        var itemCount = collListItem.get_count();
        //For each list item in the collection, mark it to be deleted
        for (var i = itemCount - 1; i >= 0; i--) {
            var oListItem = collListItem.itemAt(i);
            oListItem.deleteObject();
        };
    
        //Execute the delete operation
        clientContext.executeQueryAsync(deleteSucceeded, deleteFailed);
    }, fail_handler);  


**Note**:

In your case, the **set_viewXml** should be something like below, if you get syntax error use camel query builder tool.

    camlQuery.set_viewXml('<View><Query><Where><Eq><FieldRef Name=\'CorrespondingListID\'/>' + 
        '<Value Type=\'Text\'>somevaluefrom CorrespondingListID</Value></Eq></Where></Query></View>');

**Sample Example: using REST API** 

    function getItemsToDelete () {
        //You might have to modify this so it filters correctly on your columns
        var requestUrl = _spPageContextInfo.webAbsoluteUrl + "/_api/web/lists/getByTitle(" + myListName + ")/items?$filter=Age eq 30 and Country eq 'US'")
    
        //Return and ajax request (promise)
        return $.ajax({
            url: requestUrl,
            type: "GET",
            headers: {
                "accept": "application/json;odata=verbose",
            },
            success: function(result) {
                $.each(result.d.results, function(index, item){
                    //Note that we push the ajax-request to the array
                    //that has been declared a bit down
                    itemsToDelete.push(deleteItem(item));
                });            
            },
            error: function(error) {
                //Something went wrong when retrieving the list items
            }
        });    
    }
    
    function deleteItem (item) {
        //All SP.ListItems holds metadata that can be accessed in the '__metadata' attribute
        var requestUrl = item.__metadata.uri;
    
        return $.ajax({
            url: requestUrl,
            type: "POST",
            headers: {
                "accept": "application/json;odata=verbose",
                "X-RequestDigest": $("#__REQUESTDIGEST").val(),
                "IF-MATCH": item.__metadata.etag,
                "X-HTTP-Method": "DELETE"
            },
            success: function() {
                console.log("Item with ID " + item.__metadata.id + " successfully deleted!");
            },
            error: function(error) {
                //Something went wrong when trying to delete the item
            }
        });    
    }
    
    
    //Declare an array of deferred objects that hold a delete request
    //for each item that is to be deleted
    var itemsToDelete = [];
    
    //First get the items to delete
    $.when(getItemsToDelete()).then(function () {
        $.when.apply($, itemsToDelete).then(function(){
            console.log("All items are deleted!");
        });
    });
      

A similar question is discussed here(source):

[SharePoint 2013 ClientContext : How to DELETE specific list items by MULTIPLE CONDITION filter?][1]


  [1]: https://stackoverflow.com/questions/31452356/sharepoint-2013-clientcontext-how-to-delete-specific-list-items-by-multiple-co/31454086