In my experience it´s more of a playing clean thing than muting the strings thing. Practice alot at a really slow tempo (slow enough for you to make zero mistakes and no noise) and gradually speed up when your technique is getting better.
As for muting, I keep my picking hand rested on the bridge in a way so that if I accidently make some noise I just angle my hand more towards the strings and that way mute them.
Also: You shouldn´t only play those 2-3string sweeps, play 5-6 string sweeps as well. Here´s one I´ve been playing as practice lately
Code:
-----------------13-17p13-------------|-----------------12-15p12-------------|
--------------15----------15----------|--------------13----------13----------|
-----------14----------------14-------|-----------12----------------12-------|
--------15----------------------15----|--------14----------------------14----|
--12h17----------------------------17-|--12h15----------------------------15-|
--------------------------------------|--------------------------------------|
---------------8-12p8------------|----------------10-13p10-------------|
------------10--------10---------|-------------11----------11----------|
----------9--------------9-------|----------10----------------10-------|
-------10------------------10----|-------12----------------------12----|
--8h12------------------------12-|--8h13----------------------------13-|
---------------------------------|-------------------------------------|
-----------------13-17p13-------------|-----------------12-15p12-------------|
--------------15----------15----------|--------------13----------13----------|
-----------14----------------14-------|-----------12----------------12-------|
--------15----------------------15----|--------14----------------------14----|
--12h17----------------------------17-|--12h15----------------------------15-|
--------------------------------------|--------------------------------------|
---------------8-12p8------------|----------------10-13-10-------------||
------------10--------10---------|-------------11----------11----------||
----------9--------------9-------|----------10----------------10-------||
-------10------------------10----|-------12----------------------12----||
--8h12------------------------12-|--8h13----------------------------13-||
---------------------------------|-------------------------------------||