First of all, \biggl.
and \biggr.
do exactly nothing, except introduce unwanted opening and closing atoms (and, possibly, the relative spacing).
Second, \bigl/
makes the bigger /
an opening atom, so you should use \big
, instead.
Third, the bigger /
has wider sidebearings than the normal size symbol. If you need it only at normal and \big
size, here's a way:
\documentclass{article}
\usepackage{xparse}
\NewDocumentCommand{\dslash}{s}{%
\IfBooleanTF{#1}
{\big/\mkern-7mu\big/}
{/\mkern-6mu/}%
}
\begin{document}
$X\dslash H$
$X\dslash* H$
\end{document}

If you want other sizes, then something more complex should be devised. Here's an example:
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\dslash}{O{}}
{
\str_case:nn { #1 }
{
{}{/\mkern-6mu/}
{\big}{\big/\mkern-7mu\big/}
{\Big}{\Big/\mkern-10mu\Big/}
{\bigg}{\bigg/\mkern-14mu\bigg/}
{\Bigg}{\Bigg/\mkern-18mu\Bigg/}
}
}
\ExplSyntaxOff
\begin{document}
$X\dslash H$
$X\dslash[\big] H$
$X\dslash[\Big] H$
$X\dslash[\bigg] H$
$X\dslash[\Bigg] H$
\end{document}

biggl/
you are making/
big. Corresponding spacing also will increase. Adjust\mkern
value accordingly. But why should you usebiggl/
, I don't understand.\big
, not\bigl
. Also\biggl.
and\biggr.
are completely useless.X
andH
are replaced by something much larger. I do not see whybiggl
andbiggr
are completely useless. Can you elaborate?\biggl.
is doing?