If the “my_variable” is a string, you can take advantage of the slice filter, which treats the string as a list of characters. If it’s a set of words, the rough equivilant is truncatewords – but that doesn’t quite sound like your need.
truncatewordsalso adds an ellipsis ... at the end of the truncated result.
Usage would be something like
{{ my_variable|slice:":255" }}