You can use the camel query to get the list item based on your column value which will load only those list items which meetsmeet that criteria,then then do the delete operation as usual way.
To filter SP.ListItem's on mulitplemultiple 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>');