I want to make the following character replacements in regex-group(1):

Replace ' ' with '_'
Replace '/' with '_'
Replace ',' with '_'

I implemented that by a series of nested calls to the replace() function:

<xsl:variable name="elmt-name"

select="replace(replace(replace(regex-group(1), ' ', '_'),'/','_'), ',',
'_')"/>

So many parentheses! Really hard to understand and debug.

Is there a better way of doing this?

B  regex-group(1) => replace(' ', '_') => replace('/', '_') =>
replace(',', '_')

But as the replacement seems to be the same I wonder why you don't use
regex-group(1) => replace('[ /,]', '_')