I don't think this is currently possible in Workspace... you can do something like that using Report Builder and Excel... you can create formulas to calculate the date range based on "today()" and some if statements to dynamically calculate the to and from date ranges for your "current" and "previous" time frames.
Then you use those cells to drive the start/end dates in Report Builder, pull in your data and then present the data all in Excel; you can even schedule this to send out automatically every day.
I did something similar to this with a monthly report that looked at YTD. When the report runs on Jan 1, instead of looking at this year... I look at the full last year and previous year. Then in Feb, it calculates the YTD and Previous YTD (ie. Jan this year vs Jan last year)