Possible Clues:

• The Tramp, but not Lady
• Crosspiece found among reliquaries
• Many get longer to get upset and cross
• Cross-breed dog
• No good slicing mushroom with mixed stock
• Mixed breed
• Dog of no recognisable breed
• In among relatives, can't be sure which are his?
• It's no good tucking into mushroom of unknown variety
• Mushroom sandwiches no good — that makes us cross