Across:
1 Morality stories involving animal (FABLES) herd taken away from half-breeds ('herd' taken away from 'half-breeds' = alfbes = FABLES),
4 Heading off (b) from Hull (hull/frame = ‘body’ without ‘b’ = ODY-) on ship (-SS-) going from England (-E-) to America (-US) (ODYSSEUS) with Greek hero (ODYSSEUS),
9 It’s not in mint sauce (‘its’ not in ‘mint sauce’ = mnauce = ACUMEN) – that much is common sense (ACUMEN),
10 Boil (= anagram indicator) cream tea (cream tea = MACERATE) to infuse (MACERATE),
12 The Spanish (-EL-) get lost (-L-) in Jersey going around (‘JerseY’ going around = -J-Y) with school group (-FISH) (JELLYFISH) of swimmers – avoid them on the beach (JELLYFISH),
13 Little thanks (-TA) after (= position indicator) article (THE-) (THETA) by Greek character (8th letter of Greek alphabet = THETA),
14 Steps to be taken (CHOREOGRAPHY) by arrangement involving a twist (arrangement involving a twist / dance = CHOREOGRAPHY),
18 Trying to impress somebody by identifying big shot (NAME-DROPPING) celebrity (NAME-) taking the plunge (-DROPPING) (NAME-DROPPING),
21 Finish off (USE UP) museum – it has no wings (‘MuseuM’ it has no wings/no sides = useu = USE U-) and is open to philanthropy (open to ‘Philanthropy’ = -P) (USE UP),
22 Not having a starter (d) with meal (dinner) (‘dinner’ without ‘d’ = INNER) can be nice (Nice/France = -CITY) (INNER CITY) in a problematic built-up area (INNER CITY),
24 Way out (escape = ESCAP- E) for Bill (-AD-) inside (ESCAPADE) fooling around (ESCAPADE),
25 Accompanying (WITH-) a (-A-) lace open (‘Lace’ open = -L) (WITHAL) to boot (WITHAL),
26 It’s said (= homophone indicator) Beatrice (‘Bea’ = ‘be’ = BE-) lost (-L-) Mark (mark/score = -GRADE) (BELGRADE) in European capital (BELGRADE),
27 Curiously (= anagram indicator), US aid (US aid = SAUDI-) is endless (end ‘lesS’ = -S) (SAUDIS) for those living in Asia (SAUDIS).
Down:
1 Female (F-) friend (pal) gets back (= reverse indicator) (pal = -LAP-) with one who's bound to give you a lift (car jack = -JACK) (FLAPJACK) – it's sweet (FLAPJACK),
2 Not well (-ILL-) after (= position indicator) short (t) boxing match (bout) (‘bout’ without ‘t’ = BOU-) – take duck O (-O-) on top of nourishing (top of ‘Nourishing’ = -N) (BOUILLON) broth (BOUILLON),
3 Lament (ELEGY) in Theatre back (‘theatrE’ back = E-) stage (-LEG-) for company closing (‘companY’ closing = -Y) (ELEGY)
5 Life partner (Life and DEATH) is upset (= reverse indicator), crude (raw = WAR-), and starting row (starting ‘Row’ = -R-) with worker (-ANT) (DEATH WARRANT) – that leads to notice of the ultimate put down (DEATH WARRANT),
6 Hates (hates) boss (= anagram indicator) (hates = -EATSH-) in exchange (swop = SW-OP) (SWEATSHOP) – an exploitive place to work (SWEATSHOP),
7 Cleans up the childish mistakes (ERASER) for Regina (-R-) in flowing (= anagram indicator) saree (saree = E-ASER) (ERASER),
8 Have trouble deciding (SEESAW) in South Africa (-SA-) going after (= position indicator) spy (SEE-) from first war (first ‘War’ = -W) (SEESAW),
11 Small (S-) place for a fire (-INGLE) is taken care of (-MINDED) (SINGLE-MINDED) by concentrating on one particular thing (SINGLE-MINDED),
15 Leaving questions (Leaving Cert questions = EXAM PAPER) that could be best answered by those who should have learnt their lessons (EXAM PAPER),
16 Fiendish (fiendish) criminal (= anagram indicator) (fiendish = FINISHED) has no future? (is FINISHED),
17 Those in Mayo (those in mayonnaise = EGG YOLKS), for example (e.g. = EG-), and those around Galway (those around ‘GalwaY’ = -G Y-) people (folks), need no introduction (f) (‘folks’ without ‘f’ = -OLKS) (EGG YOLKS),
19 Bulgarian neighbour (Serb = S-ERB) admits taking top off (c) trophy (‘cup’ without ‘c’ = -UP-) (SUPERB) – it’s breathtaking (SUPERB),
20 Wild (= anagram indicator) camels (camels = MESCAL) out of drink at a watering hole? (MESCAL = alcoholic drink),
23 Some Emirati architect raised (= reverse indicator) (some ‘emirATI ARchitect’ = atiar = RAITA) by a dippy Asian type (RAITA).