I have a pivot table from which I would like to create several pivot charts of the same type (lines) but with different metrics of the pivot table.

What happens is that whenever I create a new chart and select a new metric, the previous chart also change to current metric.

How can I avoid this?

You have to use separate pivot tables.

The pivot tables/charts need to have their own pivotcaches. See https://www.contextures.com/xlpivot11.html#newcache
Also: Stop all the pivot tables applying the same grouping method •

You could try Ashish Mathur's suggestion here: Redirecting

also: Unshare a data cache between PivotTable reports - Microsoft Support